a 1200-kg pick-up truck traveling south at 15 m/s suddenly collides with a 750-kg car that is traveling east. the two vehicles stick together and slide along the road after colliding. a highway patrol officer investigating the accident determines that the final position of the wreckage after the collision is 25 m, at an angle of 50° south of east, from the point of impact. she also determines that the coefficient of kinetic friction between the tires and the road at that location was 0.40. what was the speed of the car just before the collision?
Answers
The conservation of momentum, Newton's second law and kinematics allows to find the result for the initial speed of the car is:
The speed of the car is 40 m/s at the East direction.
Given parameters
Mass of the truck M = 1200 kg. Truck speed v₀₁ = 15 m / s towards the South. Mass of the car m = 750 kg. Travel east The two vehicles unite. The braking distance d = 25m at 50º SE The friction coefficient μ = 0.40To find
The initial speed of the car.
The momentum is defined by the product of the mass and the velocity of the body, so it is a vector quantity. In the case of an isolated system the momentum is conserved.
In the attachment we see a diagram of the vehicle crash, let's write the moment for each axis.
y-axis
Initial instant. Before the shock.
[tex]p_{oy}[/tex] = M v₀₁
Final moment. After the crash
[tex]p_{fy}[/tex] = (M + m) [tex]v_{fy}[/tex]
The system is formed by the two vehicles for which during the crash it is isolated and the momentum is conserved.
[tex]p_{oy} = p_{fy} \\\\M v_{o1} = (M+m) v_{fy} \\v_{fy} = \frac{M}{M+m} \ v_{o1}[/tex]
Calculate us
[tex]v_{fy} = \frac{1200}{1200+750} \ 15[/tex]
vfx = 9.23 m / s
x-axis
Initial instant. Before the crash.
p₀ₓ = m v₀₂
Final moment. After the crash.
[tex]p_{fx}[/tex] = (M + m) [tex]v_{fx}[/tex]
The momentum is preserved.
[tex]p_{ox}= p_{fx} \\m v_{o2) = (M+m) \ v_{fx}[/tex]
Let's find the velocity just after the collision, let's use Newton's second law,
y-axis
N-W = 0
N = W = (M + m) g
x-axis
fr = (M + m) a
The friction force is the macroscopic manifestation of the interactions between the two bodies.
fr = μ N
We substitute.
μ g = a
Now we can use kinematics.
v² = v₀² - 2a d
When the vehicles stop their speed is zero.
v₀² = 2 a x
v₀ = [tex]\sqrt{2\ \mu \ g \ d}[/tex]
Let's calculate.
v₀ = [tex]\sqrt{2 \ 0.40 \ 9.8 25 }[/tex]
v₀ = 14 m / s
This is the speed of the two vehicles just after the collision, that is, let's use trigonometry to find their components.
cos 25 = [tex]\frac{v_{ox}}{v_o}[/tex]
v₀ₓ = v₀ cos 25
v₀ₓ = 14 cos 25
v₀ₓ = 12.69 m / s
We substitute in the expression of the conservation of the momentum in the x-axis.
m v₀₂ = (M + m) [tex]v_{fx}[/tex]
[tex]v_{o2} = \frac{M+m}{m} v_{fx}[/tex]
Let's calculate.
[tex]v_{o2} = \frac{1200+750}{750} \ 12.69[/tex]
vfy = 32.99 m / s = 40 m / s
In conclusion using the conservation of momentum, Newton's second law and kinematics we can find the result for the initial speed of the car is:
The speed of the car is 40 m/s at the East direction.
Learn more here: brainly.com/question/18066930
Related Questions
Which feature of a balanced chemical equation demonstrates the law of
conservation of mass?
O A. It shows the products of a chemical reaction to the right of the
reaction arrow.
B. It has coefficients to show how much of each substance a
chemical reaction uses.
C. It has the same types of atoms on both sides of the reaction
arrow.
D. It shows the reactants of a chemical reaction to the left of the
reaction arrow.
Answers
Answer:
C
Explanation:
don't worry Tama yan base sa pagkakaintindi ko
Each box weighs 10lb. The coefficient of static friction between box A and box B is 0.24, and the coefficient of static friction between box B and the inclined surface is 0.3. What is the largest angle for which box B will not slip
Answers
The largest angle for which box B will not slip is 16.7⁰.
The given parameters:
weight of box, W = 10 lbcoefficient of static friction between box A and box B, [tex]\mu_s_1[/tex] = 0.24coefficient of static friction between box B and the inclined surface, [tex]\mu_s_2[/tex] = 0.3The frictional force between box A and box B is calculated as;
[tex]F_f_1= \mu_s_1 (mg)[/tex]
The frictional force between box B and inclined surface is calculated as;
[tex]F_f = \mu_s_2 (2mg) cos(\theta)[/tex]
The net force on the boxes that results in no movement is calculated as;
[tex](2mg) sin(\theta) - F_f= 0\\\\(2mg) sin(\theta) = F_f\\\\(2mg) sin(\theta) = \ \mu_s_2 (2mg) cos(\theta)\\\\ sin(\theta) = \mu_s_2 cos(\theta)\\\\\mu_s_2 = \frac{sin(\theta)}{cos(\theta)} \\\\\mu_s_2 = tan(\theta)\\\\\theta = tan^{-1} (\mu_s_2)\\\\\theta = tan^{-1} (0.3)\\\\\theta = 16.7 \ ^ 0[/tex]
Thus, the largest angle for which box B will not slip is 16.7⁰.
Learn more about coefficient of static friction here: https://brainly.com/question/25050131
A cyclist accelerates from 0m/s to 8m/s in 3 seconds.
Answers
Answer:
the rate of acceleration is 2.6666(and so on) if thats your question
Explanation:
PLEASE ANSWER NEED HELP!!!!!!!! PLEASE THE CORRECT ANSWER!!!!!!
Jinan has high cholesterol and wants to do what he can to improve it through his diet. What would be the BEST thing for him to increase in his diet to address this issue?
A.
sugars
B.
protein
C.
carbohydrates
D.
unsaturated fat
PLEASE NO LINKS
Answers
Answer:
D. unsaturated fat
Explanation:
Unsaturated fats are considered the healthiest fats because they improve cholesterol, help reduce inflammation (a risk factor for heart disease), and help decrease the overall risk of developing heart disease. The main source of unsaturated fats are plant-based foods.
Answer:unsaturated fat
Explanation:
The c-c sigma bond in acetylene is formed by the overlap of which two orbitals.
Answers
Answer:When carbon atom tends to form single bonds then its hybridization is , when carbon atom tends to form double bond then its hybridization is and when a carbon atom is attached to a triple bond or with two double bonds then its hydridization is sp.
For example, in HCN molecule there is a triple existing between the carbon and nitrogen atom.
So, hybridization of carbon in this molecules is sp. Moreover, nitrogen atom is also attached via triple bond and it also has a lone pair of electrons. Hence, the hybridization of nitrogen atom is also sp.
Thus, we can conclude that s and p type of orbitals overlap to form the sigma bond between C and N in H−C≡N:
Explanation:
does the force change if the density change in a object
Answers
Answer:
No
Explanation:
It doesn't depend on the density
Answer:No. If you take all your masses and and squeeze them into a tiny volume,
PLEASE ANSWER THIS RIGHT ASAP
What is the correct definition of energy?
A: chemical changes
B: force × distance
C: both kinetic and potential energy
D: the ability to do work or cause change
Answers
Answer:
D: The ability to do work or cause change.
Explanation:
Energy can be defined as the ability to do work. We apply energy in basically everything we do in life, energy is needed to walk or move from one position to another, it is required to eat and do other basic things of life. The body system converts the food that is being consumed into energy, this energy can be switched from one form to another.
There are various forms of energy which include solar energy, wind energy, electrical energy, mechanical energy, kinetic energy, potential energy, etc. This form of energy can be converted from one form to another but cannot be destroyed.
Hope this helps :)
If the circumference of a space shuttle's orbit around Earth is 42,522 km and the space shuttle orbits around it 1.4 times
every hour, what is the speed of the space shuttle in km/hour? In meters/second?
Answers
Answer:
105,000km or about 65,244mi
Explanation:
If the space shuttle orbits around it 1.4 times every hour then the speed of the space shuttle in km/hour would be 595330.8 Km/hour, and its speed in meters would be 165369.67 m/s.
What is speed?The total distance covered by any object per unit of time is known as speed. It depends only on the magnitude of the moving object.
Average speed = total distance /Total time
As given in the problem If the circumference of a space shuttle's orbit around Earth is 42,522 km and the space shuttle orbits around it 1.4 times every hour, then we have to find the speed of the space shuttle in km/hour
The total distance covered by the space shuttle in an hour = 42,522×1.4
= 595330.8 Km
The speed of the space shuttle in meters/second = 595330.8 × 1000/3600
= 165369.67 m/s
Thus, the speed of the space shuttle would be 595330.8 Km/hour, and its speed in meters would be 165369.67 m/s.
To learn more about speed here, refer to the link;
brainly.com/question/7359669
#SPJ5
How to find the energy in a compressed spring.
Answers
Work is done when a spring is extended or compressed . Elastic potential energy is stored in the spring. ...
The elastic potential energy stored can be calculated using the equation:
elastic potential energy = 0.5 × spring constant × (extension) 2
which term is most applicable to a discussion of angular momentum in the context of black holes?
A: Photon
B: Curvature
C: Spin
D: Time
Answers
Answer:
c: spin
Explanation:
it's not curvature
The most applicable term to a discussion of angular momentum in the context of black holes is Spin. Thus, the correct option is C.
What is angular momentum of black holes?
Angular Momentum is defined as the property of any rotating object which is given by the product of the moment of inertia of an object and the angular velocity of the rotating object. Angular momentum is a vector quantity and it has both the magnitude and direction. The examples of angular momentum are the rotation and revolution of the Earth.
When the astronomers claim that they have estimated the spin of a black hole, this means they have measured its angular momentum. This is the total angular momentum of all the materials on the Universe that ever crossed the event horizon and got trapped inside it.
Therefore, the correct option is C.
Learn more about Angular momentum here:
https://brainly.com/question/29563080
#SPJ2
What decides free energy.
Answers
Answer: when free energy is extensive property that means its magnitude depends on the amount of a substance.
Explanation:
srry if im wrong :( .
Answer:
state of the system
Explanation:
Which do you think is easiest and hardest to keep track of: hazardous waste that is present as a gas, liquid, or solid? Why?
Answers
Answer:
probably liquid cause it can be contained easily
Compare the amplitude of these waves.
Answers
Answer:
a smooth
b less smooth
c faster
d faster than fast c
e to fast for fast
Explanation:
when a viscous fluid flows in a tube, its velocity is __________.
Answers
A bob attached to a string of length L = 1.25 m, initially found at the equilibrium
position, is given an initial velocity v = 0.8 m/s. The maximum displacement angle,
Omax, is: (Take g=10 m/s)
17
3.2
13
10.2
6.4
Clear selection
A hoh attached to a string of length 2 m is displaced by an angle of 8º and then
Answers
The maximum displacement angle of the bob is 13⁰.
The given parameters;
Length of the pendulum, L = 1.25 mInitial velocity of the bob, v = 0.8 m/sThe maximum displacement of the bob is calculated by applying the principle of conservation of energy;
[tex]P.E = K.E\\\\mgh = \frac{1}{2} mv^2\\\\h = \frac{v^2}{2g} \\\\h = \frac{0.8^2}{2\times 10} \\\\h = 0.032 \ m[/tex]
The maximum displacement angle is calculated as follows;
[tex]cos \theta = \frac{L-h}{L} \\\\cos \theta = \frac{1.25 - 0.032}{1.25} \\\\\cos \theta = \frac{1.218}{1.25} \\\\cos \theta = 0.9744\\\\\theta = cos^{-1}(0.9744)\\\\\theta = 13\ ^0[/tex]
Thus, the maximum displacement angle of the bob is 13⁰.
Learn more here:https://brainly.com/question/13981780
Which wave has the longest wavelength?
Answers
Answer:
A Wave red
Explanation:
Answer:
Answer: Wave E
Explanation:
Why because if you put each in a strait line it would have been longer
hope it helps
how have astronomers interpreted the unexpectedly fast rotation of galaxies
Answers
Answer:
There must be a lot of dark matter that can be felt but not seen
The astronomers interpreted the unexpectedly fast rotation of galaxies that there must be a large quantity of dark energy whose gravity is detectable yet invisible.
What is a galaxy?Any system of stars plus interstellar material that makes up the cosmos is referred to as a galaxy. Such assemblages are common, and many of them are so massive that they hold tens of trillions of stars.
A vast variety of galaxies, from dim, hazy dwarf objects to spectacular spiral-shaped giants, have been created by nature. Almost all galaxies seem to have formed shortly after the universe started, and they are everywhere in space, even at the farthest limits of the universe that can be seen by the most advanced telescopes.
The majority of galaxies are found in clusters, many of which are further organized into clusters that span hundreds of billions of light-years.
Since there are almost empty spaces between these so-called super clusters, the universe's overall structure resembles a network of sheets or chains of galaxies.
To know more about Galaxy:
https://brainly.com/question/2905713
#SPJ12
A father pushes his child in a cart. The cart starts to move.
Scientists can use many physical quantities to describe what is happening.
The car is placed on a ramp, which is 20 meters high. The mass of the car and the child is 100kg.
Calculate the potential energy the car will have before it is let go and the velocity the car will travel at down the ramp assuming no frictional forces.
Acceleration due to gravity (g) = 10 m/s2
Answers
The potential energy of the car when it let go is 20,000 J.
The speed of the car at the bottom of the ramp is 20 m/s.
The given parameters;
mass of the car, m = 100 kgheight of the car, h = 20 mThe potential energy of the car is calculated as follows;
P.E = mgh
P.E = 100 x 10 x 20
P.E = 20,000 J
The speed of the car at the bottom of the ramp is calculated as follows;
[tex]K.E = P.E\\\\\frac{1}{2} mv^2 = mgh\\\\v^2 = 2gh\\\\v = \sqrt{2gh} \\\\v = \sqrt{2 \times 10 \times 20} \\\\v = 20 \ m/s[/tex]
Learn more here:https://brainly.com/question/18597080
if you were planning to escape from someone and you were tied to a chair what would you do
Answers
What is the acceleration as an object goes from +20 m/s to +26 m/s over 1.4 s?
Answers
Answer:
4.3 m/s^2
Explanation:
a = vf - vi / t
26 - 20 / 1.4
= 4.28 ( round your numbers)
What does gravity, electricity, and magnesium have in common?
Answers
Answer:
magnesium (Mg), chemical element, one of the alkaline-earth metals of Group 2 (IIa) of the periodic table, and the lightest structural metal. Its compounds are widely used in construction and medicine, and magnesium is one of the elements essential to all cellular life.
Explanation:
hope it helps
2. A student becomes so excited by the whole idea of black holes that he decides to jump into one. It has a mass 10 times the mass of our Sun. What is the trip like for him
Answers
Answer:
*Disclaimer you can't actually do that, or at least not yet because the nearest black hole is at least 1,000 light years away. But if we could...
His journy would be pretty fast and horrific. For him, he would slowly be streched apart or spegetified into a string of atoms as he nears the event horizoin. But for an outside observer he would apear to go slower and slower and would never actualy reach the event horizion. This is becuase of einstines general relativity, massive objects slow time down. He would also apear to become red as the lights wavelength is streched out due to the entense gravity of the black hole.
A 0.14-MIN baseball is dropped from rest. It has a momentum of 0.90 kg⋅m/skg⋅m/s just before it lands on the ground.
For what amount of time was the ball in the air?
Answers
The time spent in the air by the ball at the given momentum is 6.43 s.
The given parameters;
momentum of the ball, P = 0.9 kgm/sweight of the ball, W = 0.14 NThe impulse experienced by the ball is calculated as follows;
[tex]Ft = \Delta P[/tex]
where;
[tex]Ft[/tex] is impulse
[tex]\Delta P[/tex] is change in momentum
The time of motion of the ball is calculated as follows;
[tex]t = \frac{\Delta P}{F} \\\\t = \frac{0.9 - 0}{0.14} \\\\t = 6.43 \ s[/tex]
Thus, the time spent in the air by the ball at the given momentum is 6.43 s.
Learn more here:https://brainly.com/question/13468390
what is the meaning of physics
Answers
Answer:
the branch of science concerned with the nature and properties of matter and energy. The subject matter of physics, distinguished from that of chemistry and biology, includes mechanics, heat, light and other radiation, sound, electricity, magnetism, and the structure of atoms.
Explanation:
what happens to light in an object that is translucent?
Answers
Translucent objects allow some light to travel through them. The light does not pass directly through the materials. It changes direction many times and is scattered as it passes through. Therefore, we cannot see clearly through them and objects on the other side of a translucent object appear fuzzy and unclear.
PLEASE ANSWER NEED HELP!!!!!!!! PLEASE THE CORRECT ANSWER!!!!!!
Jose’s doctor recommends that he add more cardio to his exercise routine. Which exercise would be the BEST choice?
A.
ballet
B.
jogging
C.
bowling
D.
volleyball
PLEASE NO LINKS OR I WILL REPORT YOU
Answers
Explanation:
I learned in PE
Answer:
jogging
Explanation:
Jogging is often defined as running at a pace less than 6 miles per hour (mph), and it has some significant benefits for people who want to improve their health without overdoing it.
Calculate the weight of an object that displaces 3 m2 of water and exerts a pressure of 500 Pa (500 N/m ).
Answers
The weight of the object from the information provided in the question is 1500 N.
We know that pressure = Force/area. We have the following information from the question;
Pressure =500 Nm-2
Area = 3 m2
Hence;
Force = Pressure × area
Force = 500 Nm-2 × 3 m2
Force = 1500 N
Hence, the weight of the object is 1500 N
Learn more: https://brainly.com/question/8646601
A sports car accelerates from 0 to 60mph ,27 m/s ,in 6.3 secounds .The car exerts a force of 4106N . What is the mass of the car
Answers
The car accelerates 60 mph in 6.3 seconds. Thus, the acceleration is [tex]\frac{60}{6.3}[/tex]. [tex]f=ma[/tex], so [tex]4106 = m(\frac{60}{6.3})[/tex], so [tex]m=431.13[/tex].
What is a net force on an object that has a mass of 20.0 kg, an applied force of 100 n moving on a surface with a friction coefficient of 0.21?
Answers
The net force on the object as described is; 58.84N
Two forces acting on the object are;
The applied force and the frictional force.In essence; the frictional force can be evaluated as;
Frictional force; = coefficient × Weight of object.Frictional force = 0.21 × 20 × 9.8.Frictional force = 41.16NThe Net force = Applied force - frictional forceNet force = 100 - 41.16NNet Force = 58.84 N.
Read more:
https://brainly.com/question/94428
A car starts from rest and accelerates at 2.5m/s^2 for 2s. What is the final velocity of the car
Answers
Answer:
5m/s ez
Explanation:
plz make me brainliest