Yes, if one follows the mentioned steps, they could determine the toy car's acceleration from the data of time taken in the video.
a = v / t
v = d / t
a = Acceleration
v = Velocity
d = Distance
t = Time
d = 1 m
Let the video time recorded from the video be x s.
t = x s
v = 1 / x
a = 1 / x / x
a = 1 / x² m / s²
Velocity is the rate of change of distance. Its unit is m / s. It is denoted as v. Acceleration is defined as the rate of change in velocity with respect to time. Its unit is m / s². It is denoted as a.
Therefore, if I follow steps given, I could determine the acceleration of the toy car as 1 / x² m / s²
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what voltage was needed for 2 amps to flow through a 600 lamp
Answer:
See below
Explanation:
Is that 600 WATT lamp ? If so:
power = I V
600 w = 2 A * v
v = 300 v
A car starts from rest and travels for 4.9 s with a uniform acceleration of +1.4 m/s2. The driver then applies the brakes, causing a uniform acceleration of -1.9 m/s2. The brakes are applied for 1.60 s.
(a) How fast is the car going at the end of the braking period?
(b) How far has the car gone from its start?
The car is going at speed of 3.82 m/s at the end of the breaking period and the car traveled the distance from the start is 25.33 m.
What is Acceleration?The rate of change in an object's velocity concerning time is known as acceleration in mechanics. The vector quantity of accelerations. The direction of the net force that is acting on an object determines its acceleration.
Since acceleration has both a magnitude and a direction, it is a vector quantity. Velocity is a vector quantity as well. The definition of acceleration is the change in velocity vector over a time interval divided by the time interval.
According to the question, the given values are :
Time, t₁ = 4.9 s
Time, t₂ = 1.60 s
Acceleration, a₁ = 1.4 m/s²
Acceleration, a₂ = -1.9 m/s²
Initial Velocity, u = 0 m/s
(a)
By the Equation of motion,
v = u + a₁t₁
v = 0 + (1.4)(4.9)
v = 6.86 m/s.
Now, the velocity of the car at the end of the breaking period :
v' = v + a₂t₂
v' = 6.86 + (-1.9)(1.60)
v' = 3.82 m/s.
(b)
s₁ = ut₁ + 1/2 a₁t₁²
s₁ = 0 + 1/2 (1.4)(4.9)²
s₁ = 16.8 m.
Now for the decelerated motion :
s₂ = vt₂+1/2 a₂t₂²
s₂= 6.86(1.60) + 1/2 (-1.9)(1.60)²
s₂ = 8.53 m.
So, total distance covered from the start, D :
D = s₁ + s₂
D = 16.8 + 8.53
D = 25.33 m.
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while test flying the new f-22 raptor fighter jet, test pilot bob put the plane in a horizontal loop while flying at the speed of sound (343 m/s). what is the minimum radius that the plane can fly if bobs centripetal acceleration cannot exceed 5g (5 times the acceleration due to gravity)?
Given
v = 343 m/s
ac = 5g
ac = 5*9.8 m/s^2
ac = 49 m/s^2
where,
v: velocity
ac = centripetal aceleration
Procedure
We call the acceleration of an object moving in uniform circular motion—resulting from a net external force—the centripetal acceleration ac; centripetal means “toward the center” or “center seeking”.
Formula
[tex]\begin{gathered} a_c=\frac{v^2}{r} \\ r=\frac{v^2}{a_c} \\ r=\frac{(343m/s)^2}{49m/s^2} \\ r=2401\text{ m} \end{gathered}[/tex]The minimum radius not to exceed the centripetal acceleration is 2401 m.
Is water in the air a source of radiation or convection?
How is air in a hot air Ballon convection?
Answer: Convection
Explanation: in its simplest form is the transfer of heat through circulating air and liquids, this works inside of a hot air balloon by heating the inside of the air with a burner located at the bottom of the balloon, this then makes the air inside of the balloon less dense or lighter than the cooler air on the outside, causing the balloon to float upwards.
draw a molecule of carbon monoxide, CO, has ____ atoms.
you jump off a cliff and accelerate at 9.8 m/s^2 due to gravity. How fast are you falling after 12.0 seconds?
By the speed of 117.6 m/s you falling after 12.0 seconds.
Free fall formula,
v = -gt
v = velocity of free fall
g = acceleration due to gravity, Given = 9.8 m/[tex]s^{2}[/tex]
t = time, Given = 12s
Put these values in formula, v = -gt
v = - 12 × 9.8
v = 117.6 m/s.
Hence, by the speed of 117.6 m/s you falling after 12.0 seconds.
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find the components of each vector
Answer: The direction of the resultant can be determined by finding the angle that the resultant makes with either the north-south or the east-west vector. The diagram at the right shows the angle theta (Θ) marked inside the vector addition triangle. This angle theta is the angle that the resultant makes with west.
Explanation: hope this helps.
What are three ways that velocity can change
Answer:
Velocity is a vector quantity, meaning it is dependent on both magnitude and direction of motion. It can be changed by
1. Changing its magnitude (i.e. speed)
2. Changing the direction of motion
3. Changing both magnitude and direction.
velocity can change the three ways are, It has the ability to change direction, speed up, or slow down.
VelocityVelocity can be defined as the rate at which something moves in a specific direction. as the speed of a car driving north on a highway or the pace at which a rocket takes off. Because the velocity vector is scalar, its absolute value magnitude will always equal the motion's speed. The SI unit of velocity is metre per second (m/s). A different way to express velocity magnitude is in centimeters per second (cm/s).velocity is the quickness or speed of motion, action, or operation. A measurement of a body's rate of motion in physics is the rate at which its location changes over time in a certain direction.To learn more about Velocity refer:
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Can someone pls help meee
In the diagram the numbered parts are:
1. Muscle belly
2. Fascicle
3. Epimysium
4. Myofibril
5. Muscle fiber
6. Endomysium
7. single muscle fiber
8. H zone
9. Z disc
10. Sarcolemma
Explain anatomy of muscle?Each muscle is made up of fascicles, which are groups of muscle fibers surrounded by a connective tissue layer called perimysium. Within each fascicle, there are multiple units of individual muscle fibers surrounded by endomysium, a connective tissue sheath.A typical skeletal muscle has three parts: the origin, the belly, and the insertion. The belly is the widest part of a muscle. The tendon attachments are dealt with at the origin and insertion.
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Certain iguanas have been observed to run as fast as 10.0m/s.Suppose an iguana runs in a straight line at this speed for 5.00 s. The direction of motion makes an angle of 30.0° to the east of north. Find the value of the iguana’s northward displacement.
The value of the iguana’s northward displacement is 1 meter.
The velocity V of iguana is 10m/s.
The time for which iguana runs is 5 seconds.
The angle it is making with the north is 30°.
The velocity of iguana will have two components now,
One along east and one along north.
The component along east is Vcos(30°).
And the component along north is Vsin(30°).
The horizontal displacement of the iguana is,
Northward displacement = northward velocity × time.
The northward velocity is 10sin(30°).
Time is 5 seconds no matter where the iguana moves.
So,
Northwards displacement = 10sin(30°)/5
Northwards displacement = 10/10 = 1m
The displacement in north is 1 meter.
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1 (a) A large stone, initially at rest, falls from the top of a building. The stone takes 3.2s to fall to the ground. For this stone, air resistance can be ignored.
(i) Stating the formula that you use, show that the speed of the stone when it hits the ground is 32 m/s.
The formula that can be used to show that the speed of the stone when it hits the ground is 32 m/s is v = u + at
According to equations of motion,
v = u + at
v = Final velocity
u = Initial velocity
t = Time
a = Acceleration due to gravity
t = 3.2 s
a = 10 m / s²
v = 0 + ( 10 * 3.2 )
v = 32 m /s
Equations of motion are used to describe the position of a moving object in a constantly accelerated manner. The position can be described using acceleration, velocity, displacement and time.
Therefore, the formula that can be used to show that the speed of the stone when it hits the ground is 32 m/s is v = u + at
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What does the square mean in Galileo’s equation? ∆x = 1/2 a(∆t)^2
The square in Galileo’s equation means that for every given distance traveled by a falling body, the time taken is squared.
What is Galileo’s equation?Galileo’s equation is an equation that states that the distance traveled by a falling body is directly proportional to the square of the time it takes to fall.
Mathematically, Galileo’s equation is given below:
∆x = ¹/₂ a * (∆t)²
where,
∆x = the change in distancea = the acceleration due to gravity∆t² = square of the change in time.Galileo’s equation is used to calculate the distance traveled by a falling body under gravity for a given time.
It is also used to determine the time of fall from a given height.
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An object is suspended from two cables that meet at a point above the object. One cable pulls with a force modeled by F1 = −78i + 44j. The other cable pulls with a force modeled by F2 = 87i + 80j. What is the angle between the cables? Round to the nearest degree.150°108°104°71°
From the information given, the forces are
F1 = −78i + 44j
F2 = 87i + 80j
We would apply the dot product.
F1F2 = <- 78, 44> * <87i, 80j>
F1F2 = - 78(87) + 44(80) = - 6786 + 3520
F1F2 = - 3266
|F1| = √[(- 78)^2 + 44^2] = √8020
|F2| = √[87^2 + 80^2] = √13969
The angle between them is
θ = Cos^-1[F1F2/(|F1||F2|)
θ = Cos^-1(- 3266/√8020 * √13969
θ = Cos^-1(- 0.30856)
θ = 108 degrees
the angle between the cables is 108 degrees
pressure exerted on a surface
Answer:
Pressure is defined as the force exerted on a surface divided by the area over which that force acts. Force is measured in units of Newtons (N), named after the famous scientist Isaac Newton. Area is typically measured in units of meters squared (m2).
Find the resultant of the following vectors:
ASAPPPPP!!!!!
The resultant vector is middle line which is the longest line representing the single effect of the two vectors at both ends.
What is resultant vector?A resultant vector is defined as a single vector that produces the same effect as the two or more vectors combined together.
A resultant vector is usually, drawn to join the head of the first vector to the tail of the second in a triangle method of vector addition.
Also, a resultant vector can be determined by applying parallelogram law of vector addition.
Mathematically, a resultant vector can be determined using this formula,
R² = a² + b² - 2ab cosθ
where;
a is the first vectorb is the second vectorθ is the angle between vector a and vector bA resultant vector is always bigger than the two vectors acting together.
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module 1 question 15
A swimmer bounces straight up from a diving board and falls feet first into a pool. She starts with a velocity of 5.00 m/s, and her takeoff point is 1.90 m above the pool.
(a) How long are her feet in the air?
s
(b) What is her highest point above the board?
m
(c) What is her velocity when her feet hit the water?
m/s
( a ) T = ( [tex]u_{y}[/tex] + √ [tex]u_{y}[/tex]² + 2 g H ) / g
T = Total time taken
g = Acceleration due to gravity
H = Height above the ground
u = 5 m / s
H = 1.9 m
g = 9.8 m / s²
[tex]u_{y}[/tex] = Y-component of initial velocity
θ = 90° ( Since she bounces straight up )
sin θ = [tex]u_{y}[/tex] / u
[tex]u_{y}[/tex] = 5 * sin 90°
[tex]u_{y}[/tex] = 5 m / s
T = ( 5 + √ 5² + ( 2 * 9.8 * 1.9 ) ) / 9.8
T = ( 5 + √ 62.24 ) / 9.8
T = 12.89 / 9.8
T = 1.32 s
( b ) v² = u² + 2 a s
v = Final velocity
u = Initial velocity
s = Displacement
Consider the y-components until the swimmer reaches the highest point of her motion,
[tex]v_{y}[/tex] = 0
a = - 9.8 m / s²
[tex]u_{y}[/tex] = 5 m / s
0 = 5² + ( 2 * - 9.8 * s )
19.6 s = 25
s = 1.28 m
Maximum height reached = 1.9 + 1.28
Maximum height reached = 3.18 m
( c ) V = √ [tex]V_{x}[/tex]² + [tex]V_{y}[/tex]²
V = Final velocity
[tex]V_{x}[/tex] = X-component of final velocity
[tex]V_{y}[/tex] = Y-component of final velocity
[tex]V_{x}[/tex] = [tex]U_{x}[/tex] ( Since there is no external force acting on x-direction )
cos θ = [tex]U_{x}[/tex] / u
[tex]U_{x}[/tex] = cos 90° * 5
[tex]U_{x}[/tex] = 0
[tex]V_{y}[/tex] = [tex]U_{y}[/tex] + a t
[tex]V_{y}[/tex] = 5 + ( - 9.8 * 1.32 )
[tex]V_{y}[/tex] = 5 - 12.94
[tex]V_{y}[/tex] = - 7.94 m / s
V = √ 0 + ( - 7.94 )²
V = √ 63.04
V = 7.94 m / s
Therefore,
Her feet are in the air for 1.32 sHer highest point above the board from the ground = 3.18 mHer velocity when her feet hit the water = 7.94 m / sTo know more about Projectile launched from a height
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(1) If a man lifts a a 20-kg
bucket from a well and does 6
kJ of work, how deep is the
well? Assume the speed o the
bucket remains constant as it is
lifted.
If a man lifts a a 20-kg bucket from a well and does 6 kJ of work, the well will be 30.6 m deep.
W = m g h
W = Work
m = Mass
g = Acceleration due to gravity
h = Height
m = 20 kg
g = 9.8 m / s²
W = 6 KJ
W = 6000 J
h = W / m g
h = 6000 / 20 * 9.8
h = 30.6 m
W = m g h is derived from W = F * d. According to Newton's second law of motion, F = m a. Since the object is moving vertically upwards, a = g. Therefore, F = m g and hence W = m g h
Therefore, the well is 30.6 m deep
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SORRY IF IN WRONG SECTION. ANSWER FOR 50 POINTS. 1. The chemical process by which your body breaks down the nutrients in foods to release energy (1 point) for the cells in your body describes OCalories Ocholesterol Ometabolism Onutrition
Metabolism is the chemical process by which your body breaks down the nutrients in foods to release energy for the cells in your body (Option 3).
What is Metabolism?The term Metabolism makes reference to all chemical reactions by which the body can obtain energy from foods by breaking them down into smaller elements. The breakdown of chemical bonds releases energy, which is used to generate Adenosine triphosphate, the energy coin of the cells.
Metabolism has two major categories:Catabolism or metabolic pathways where foods are reduced to smaller molecules that are used for oxidation and thus the production of energy.Anabolism or metabolic pathways aimed at generating complex molecules from simpler ones.Therefore, we can conclude that metabolism refers to the groups of pathways by which an organism breaks down nutrients such as proteins or carbohydrates in order to obtain energy for cells and perform diverse activities (e.g. growth, differentiation, etc)
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What mathematical relationship between variables is suggested by a graph showing an L-shaped hyperbola that drops and flattens quickly?
Inverse (simple)
Inverse-squared
Linear (direct)
Quadratic (power)
The mathematical relationship between variables is suggested by a graph showing an L-shaped hyperbola that drops and flattens quickly is option A: Inverse (simple).
What is a inverse relationship in math?When two variables change in an inverse relationship, they do so in the opposite directions: one increases while the other drops, and vice versa. Y declines as X rises in an inverse relationship. An inverse relationship always has a negative slope on a graph.
A function that can be altered into another function is said to be one that can be seen as an inverse function or what we call the anti-function.
Therefore, Inverse operations are a class of mathematical operations where one operation cancels out the effects of another and it best shows L-shaped hyperbola.
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Answer:
B. Inverse-squared
Explanation:
I took the physics exam
Which of the following does not correctly describe each given vector in terms of the unit vectors? (Note that each grid line is half of a unit.)
(Will give brainyist)
Not sure how to do part a, b and c
Variables typically consist of space, time, and occasionally parts of momentum. The bicycle eventually travels at 13.8 m/s.
what exactly does momentum mean?According to Newtonian mechanics, an object's mass and velocity are combined to form its linear momentum, translational momentum, or just momentum. As a vector quantity with both a magnitude and a direction, it has both. When an object's mass (m) and velocity (v), another vector quantity, are known, the object's momentum (p) is also known.
what is significance of momentum?An object's mass, velocity, and direction are related by the concept of momentum. Force is produced whenever momentum changes. As a result, the force pushing against the object is identified by a change in momentum.
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A train accelerates from 36 km/h to 54 km/h in 10 seconds. Find the acceleration and distance traveled by the train.
In your own words, answer the following 3 questions about an object experiencing red shift? 1. Describe the motion of an object experiencing red shift? 2. What is happening to its wavelength and frequency? 3. Why?
1. When an object is moving away from us, the light from the object is known as redshift, and when an object is moving towards us, the light from the object is known as blueshift.
2. A wavelength increases in size, and its frequency, and energy decrease.
3. The frequency of a wave increases, and its wavelength decreases.
Redshift is an important term for astronomers. The term can be taken literally. The wavelengths of light are stretched and perceived as shifting toward the red portion of the spectrum. The same thing happens to sound waves when the source moves relative to the observer.
As the wave frequency decreases, the wavelength increases as long as the wave velocity remains constant. If the wave speed stays the same as the frequency decreases, it means that fewer wave peaks or troughs pass through a given point in a given time period. The number of complete wavelengths in a given unit of time is called frequency. Frequency and energy decrease with increasing wavelength.
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An adventurous archaeologist crosses between two rock cliffs by slowly going hand-over-hand along a rope stretched between the cliffs. He stops to rest at the middle of the rope. The rope will break if the tension in it exceeds 2.55×10^4 N, and our hero's mass is 85.6 kg.
A) If the angle between the rope and the horizontal is θ = 10.5∘, find the tension in the rope.
B) What is the smallest value the angle θ can have if the rope is not to break?
The tension in the rope and the smallest value the angle θ can have if the rope is not to break
[tex]\theta=0.966 \textdegree[/tex]T=2232 NThis is further explained below.
The smallest value the angle θ can have if the rope is not to break:Generally, the equation for the tension is mathematically given as
[tex]2 T sin \theta = m g[/tex]
Therefore
2*T*sin(11.1) = 87.6 * 9.81
T=2232 N
the tension in the rope is T=2232 N
b)
Generally, the equation for the angle is mathematically given as
[tex]2*2.55E4*sin \theta = 87.6*9.81[/tex]
Therefore
[tex]\theta = arcsin( \frac{87.6*9.81}{(2*2.55E4))}[/tex]
[tex]\theta=0.966 \textdegree[/tex]
In conclusion, The smallest value the angle θ can have if the rope is not to break is
[tex]\theta=0.966 \textdegree[/tex]
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The table shows the mass of and acceleration due to gravity for several
planets in the solar system. If air resistance is ignored, on which planet would
a space probe with a mass of 250 kg a have the highest speed after falling 25
m?
Planet
Mass, 1024 kg
Acceleration due to gravity,
m/s-
Venus
4.87
8.9
Earth
5.97
9.8
Uranus
86.8
8.7
Saturn
568
A. Earth
• B. Venus
• C. Saturn
O D. Uranus
Mass does not affect the speed of falling objects, As there is only gravity acting on them.
The mass of Uranus exists: 8.681 × 10²⁵kg
The radius of Uranus exists: 15,759.2 miles
What is meant by the acceleration due to gravity?Acceleration due to gravity exists as the acceleration gained by an object due to gravitational force.
Its SI unit exists m/s2. It contains both magnitude and direction.
The planet would be a space probe with a mass of 250Kg
The distance is 25m.
Mass does not affect the speed of falling objects, As there is only gravity acting on them.
The mass of Uranus exists m = 8.681 × 10²⁵kg
The radius of Uranus exists: 15,759.2 miles
Therefore, the correct answer is option D. Uranus
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Complete the following table about metric units
The change in the speed of the object is constant with constant increment of 5 m/s.
What is change in speed?The change in the speed of an object is the rate at which the distance covered by the object changes with time.
The change in the speed of the object at various time is calculated as follows;
at time, t = 0 second, change in speed (Δv) = 0
at time, t = 1 second, change in speed (Δv) = 5 m/s - 0 m/s = 5 m/s
at time, t = 2 seconds, change in speed (Δv) = 15 m/s - 5 m/s = 10 m/s
at time, t = 3 seconds, change in speed (Δv) = 30 m/s - 15 m/s = 15 m/s
at time, t = 4 seconds, change in speed (Δv) = 50 m/s - 30 m/s = 20 m/s
at time, t = 5 seconds, change in speed (Δv) = 75 m/s - 50 m/s = 25 m/s
Thus, we can conclude that, the data given in the table has time which increased gradually while the speed also increase gradually but with a constant increment.
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A mineral that forms when water evaporates is
a Gold
b Silver
C Halite
d Diamond
Answer:
Halite
Explanation:
calculate the force exerted between two charged objects seperated by a distance of 0.6 m. one object has a charge of -5 C and the other has a charge of +2.0 C
The electrostatic force of repulsion between the two charges is equal to 0.25 x 10¹¹ N.
What is the formula to calculate the force between 2 point charges?
The coulomb's law is used to find the force between two point charges. The force can be calculated using the formula -
F = 1/4πε₀ |Q₁||Q₂|/r²
Given is two charged objects separated by a distance of 0.6 m such that one object has a charge of -5 C and the other has a charge of +2C.
The electrostatic force of repulsion between the two charges is given by-
F = 1/4πε₀ |Q₁||Q₂|/r²
F = 9 x 10⁹ x (5 x 2)/(0.6)²
F = 90 x 10⁹/0.36
F = 9 x 10¹¹/36
F = 0.25 x 10¹¹ N
Therefore, the electrostatic force of repulsion between the two charges is equal to 0.25 x 10¹¹ N.
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Disturbed by speeding cars outside his workplace, Nobel laureate Arthur Holly Compton designed a speed bump (called the "Holly hump") and had it installed. Suppose a 1800-kg car passes over a hump in a roadway that follows the arc of a circle of radius 21.4 m as in the figure below.(a) If the car travels at 26.6 km/h what force does the road exert on the car as the car passes the highest point of the hump?(b) What is the maximum speed the car can have without losing contact with the road as it passes this highest point?
ANSWER
[tex]\begin{gathered} (a)13,046N \\ (b)14.5m\/s\text{ or }52.2km\/h \end{gathered}[/tex]EXPLANATION
Parameters given:
Mass of the car, m = 1800 kg
Radius of arc, r = 21.4 m
(a) First, let us make a free body sketch of the problem:
where N = force exerted by the road on the car
W = weight of the car
v = velocity of the car
First, let us convert the given velocity to meters per second:
[tex]\begin{gathered} v=26.6\cdot\frac{1000}{3600} \\ v=7.39m\/s \end{gathered}[/tex]The centripetal force acting on the car as it moves in the semi-circular arc is given by:
[tex]F=\frac{mv^2}{r}[/tex]The total forces acting on the car is:
[tex]N-W+F=0[/tex]This implies that:
[tex]\begin{gathered} N=W-F \\ N=mg-\frac{mv^2}{r} \\ N=(1800\cdot9.8)-\frac{1800\cdot7.39^2}{21.4}=17,640-4,593.54 \\ N=13,046N \end{gathered}[/tex]That is the force that the road exerts on the car.
(b) At the maximum speed, the car will start to lose contact with the road at N = 0:
[tex]\begin{gathered} \Rightarrow0=W-F \\ 0=mg-\frac{mv^2_m}{r} \\ \Rightarrow\frac{mv^2_m}{r}=mg \\ \Rightarrow v^2_m=gr \\ \Rightarrow v_m=\sqrt[]{gr} \end{gathered}[/tex]Substitute the values of g and r to solve for maximum speed, vm:
[tex]\begin{gathered} v_m=\sqrt[]{9.80\cdot21.4} \\ v_m=\sqrt[]{209.72} \\ v_m=14.5m\/s \end{gathered}[/tex]In km/h, that is:
[tex]\begin{gathered} 14.5\cdot\frac{3600}{1000} \\ 52.2km\/h \end{gathered}[/tex]That is the maximum speed that the car can have.
6. An astronaut and equipment weigh 2,156 N on Earth. Weightless in space, the astronaut throws away
a 5.0 kg wrench with a velocity of 5.0 m/s. What is the resulting velocity of the astronaut in the opposite
direction?
Answer:
One of the first things we need to know is the mass of the astronaut and equipment combined. Weight is given by the formula:
W = m x g, where m is the mass of the object(kg) and g is the gravitational acceleration on Earth's surface(9.8 m/s^2)
Knowing the weight of the astronaut and equipment, we get:
m = W / g
m = 2,156 N / 9.8 m/s^2 ( ^2 represents the power of 2)
m = 219.9 kg
Now, one last thing we need to know is the resulting velocity of the astronaut in the opposite direction. Once the astronaut throws the wrench from their equipment, according to the 3rd law of motion, the astronaut and the wrench will move in opposite directions because the astronaut pushed the wrench, and in return, the astronaut is pushed by the wrench. Having all these, we need to work with momentum.
p = m * v, where p is the object's momentum, m is mass and v is its velocity
let's call [tex]m_{a}[/tex] the astronaut's mass(combined with their equipment, including the wrench since it's initially part of the equipment)
[tex]m_{w}[/tex] = 5.0 kg is the wrench's mass
[tex]v_{wrench}{[/tex] = 5.0 m/s is the wrench velocity after it was thrown
The astronaut's momentum(before the thrown wrench): [tex]p_{before}=m_{a} * 0 = 0[/tex], because the astronaut's initial velocity is zero(including the equipment and wrench)
The astronaut threw the wrench. Therefore, we get the following momentum: [tex]p_{after} = m_{w} * v_{wrench} + (m_{a} - m_{w} ) * v_{after}[/tex]
The reason why we subtract the astronaut and equipment mass from the wrench's mass is that the astronaut and the equipment move independently from the wrench, therefore we exclude the wrench's mass.
The 3rd law of motion also implies that the total momentum of a system of objects interacting(colliding against one another) doesn't change. Therefore:
[tex]p_{before} = p_{after}[/tex]
Plugging all the values, we get:
5.0 kg * 5.0 m/s + (219.9 kg - 5.0 kg) * [tex]v_{after}[/tex] = 0
Solving the above equation, we get that the resulting velocity of the astronaut in the opposite direction is:
[tex]v_{after}=-8.596 m/s[/tex]
Note: The minus denotes the opposite direction the astronaut has after it was pushed by the wrench.