Answer:
h = 90.10 m
Explanation:
Given that,
A man is standing near the edge of a cliff 85 meters high, h₀ = 85 m
The initial speed of the stone, u = 10 m/s
The path followed by the projectile is given by :
[tex]h(t)=-4.9t^2+10t+85[/tex] ....(1)
For maximum height,
Put dh/dt = 0
So,
[tex]\dfrac{dh}{dt}=-9.8t+10=0\\\\t=\dfrac{10}{9.8}\\\\=1.02\ s[/tex]
Put the value of t in equation (1).
[tex]h(t)=-4.9(1.02)^2+10(1.02)+85\\\\=90.10\ m[/tex]
So, the maximum height of the stone is equal to 90.10 m.
A Michelson interferometer operating at a 600nm wavelength has a 2.02-cm-long glass cell in one arm. To begin, the air is pumped out of the cell and mirror M2 is adjusted to produce a bright spot at the center of the interference pattern. Then a valve is opened and air is slowly admitted into the cell. The index of refraction of air at 1.00 atm pressure is 1.00028.
How many bright-dark-bright fringe shifts are observed as the cell fills with air?
Answer:
19
Explanation:
Given that:
wavelength = 600 nm
Distance (d) = 2.02 cm = 2.02 × 10⁻² m
refraction index of air (n) = 1.00028
Pressure = 1.00 atm
∴
The number of bright-dark-bright fringe shifts can be determined by using the formula:
[tex]\Delta m = \dfrac{2d}{\lambda} (n -1 ) \\ \\ \Delta m = \dfrac{2\times2.02 \times 10^{-2}}{600\times 10^{-9}} (1.00028 -1 ) \\ \\ \Delta m = 67333.33 \times 10^{-5}(1.00028 -1) \\ \\ \Delta m = 67333.33 \times 10^{-5}(2.8\times 10^{-4}) \\ \\ \Delta m = 18.853 \\ \\ \mathbf{\Delta m = 19}[/tex]
A motorist travels due North at 90 km/h for 2 hours. She changes direction and travels West at 60 km/for 1 hour.
a) Calculate the average speed of the motorist [4]
b) Calculate the average velocity of the motorist.
Answer:
a. 50km/hr.
b. 10km/hr
Explanation:
Average speed, which is calculated by dividing the total distance travelled by the time interval as follows:
Average speed = total distance travelled ÷ time
Average velocity is calculated by dividing the total displacement by the time interval as follows:
Average velocity = change in displacement (∆x) ÷ time (t)
According to this question, a motorist travels due North at 90 km/h for 2 hours. She then changes direction and travels West at 60 km/for 1 hour.
Total distance of this journey is 90 + 60 = 150
Total time taken = 1 + 2 = 3hours
Average speed = 150/3
= 50km/hr.
b.) Average velocity = x2 - x1/t
Average velocity = 90 - 60/3
= 30/3
= 10km/hr
A 7.5-kg rock and a 8.9 × 10-4-kg pebble are held near the surface of the earth. (a) Determine the magnitude of the gravitational force exerted on each by the earth. (b) Calculate the magnitude of the acceleration of each object when released.
Answer:
F' = 73.7 N
F = 8.749×10⁻³ N
a' = a = 9.83 m/s²
Explanation:
(a)
For the rock
Applying
F' = Gm'm/r²................... Equation 1
Where F = magnitude of the gravitational force on the rock, G = Gravitational constant, m' = mass of the rock, m = mass of the earth, r = radius of the earth.
From the question,
Given: m' = 7.5 kg
Constant: m = 5.98×10²⁴ kg, G = 6.67×10⁻¹¹ Nm²/kg², r = 6.37×10⁶ m
Substitute these values into equation 1
F' = 6.67×10⁻¹¹ (7.5)(5.98×10²⁴)/(6.37×10⁶)²
F' = 7.37×10¹ N
F' = 73.7 N
Also, For the pebble,
F = GMm/r².............. Equation 2
Where M = mass of the pebble, F = Gravitational force exerted on the pebble by the earth
Given: M = 8.9×10⁻⁴ kg,
Substitute into equation 2
F = 6.67×10⁻¹¹(8.9×10⁻⁴)(5.98×10²⁴)/(6.37×10⁶)²
F = 8.749×10⁻³ N
(b)
For the rock,
a' = F'/m'
Where a' = magnitude of the acceleration of the rock
a' = 73.7/7.5
a' = 9.83 m/s²
For the pebble,
a = F/M
Where a = acceleration of the pebble
a = (8.749×10⁻³)/(8.9×10⁻⁴)
a = 9.83 m/s²
a mass of air occupied 150 cm3 at 20°c and 760 mmhg pressure. calculate it volume when heated to 100°c and constant pressure
Answer:
191 cm³
Explanation:
We'll begin by converting celsius temperature to Kelvin temperature. This can be obtained as follow:
T(K) = T(°C) + 273
Initial temperature (T₁) = 20 °C
Initial temperature (T₁) = 20 °C + 273
Initial temperature (T₁) = 293 K
Final temperature (T₂) = 100 °C
Final temperature (T₂) = 100 °C + 273
Final temperature (T₂) = 373 K
Finally, we shall determine the final volume of the air. This can be obtained as follow:
Initial volume (V₁) = 150 cm³
Initial temperature (T₁) = 293 K
Final temperature (T₂) = 373 K
Pressure = constant
Final volume (V₂) =?
V₁/T₁ = V₂/T₂
150 / 293 = V₂ / 373
Cross multiply
293 × V₂ = 150 × 373
293 × V₂ = 55950
Divide both side by 293
V₂ = 55950 / 293
V₂ ≈ 191 cm³
Thus, the final volume of the air is 191 cm³
Calculate the battery voltage to send 2.5 A of current through a light bulb with 3.6 ohms of resistance
Answer:
9 volts
Explanation:
[tex]v = i \times r \\ v = 2 .5 \times 3.6 \\ v = 9[/tex]
calculate the correct fuse that should be used for a 230V,1KW electric hair dryer.
Answer: 4 A
Explanation:
Given
Voltage [tex]V=230\ V[/tex]
Power [tex]P=1\ kW[/tex]
Power is given by [tex]P=VI\\[/tex]
Insert the values
[tex]\Rightarrow 1000=230\times I\\\\\Rightarrow I=\dfrac{1000}{230}\\\\\Rightarrow I=3.84\ A[/tex]
The rating of fuse is slightly higher than the normal operating conditions. Therefore, a 4 A fuse should be used here.
A mass of 4 kg is traveling over a quarter circular ramp with a radius of 10 meters. At the bottom of the incline the mass is moving at 21.3 m/s and at the top of the incline the mass is moving at 2.8 m/s. What is the work done by all non-conservative force in Joules?
Answer:
499.7 J
Explanation:
Since total mechanical energy is conserved,
U₁ + K₁ + W₁ = U₂ + K₂ + W₂ where U₁ = potential energy at bottom of incline = mgh₁, K₁ = kinetic energy at bottom of incline = 1/2mv₁² and W₁ = work done by friction at bottom of incline, and U₂ = potential energy at top of incline = mgh₂, K₁ = kinetic energy at top of incline = 1/2mv₂² and W₂ = work done by friction at top of incline. m = mass = 4 kg, h₁ = 0 m, v₁ = 21.3 m/s, W₁ = 0 J, h₂ = radius of circular ramp = 10 m, v₂ = 2.8 m/s, W₂ = unknown.
So, U₁ + K₁ + W₁ = U₂ + K₂ + W₂
mgh₁ + 1/2mv₁² + W₁ = mgh₂ + 1/2mv₂² + W₂
Substituting the values of the variables into the equation, we have
mgh₁ + 1/2mv₁² + W₁ = mgh₂ + 1/2mv₂² + W₂
4 kg × 9.8 m/s²(0) + 1/2 × 4 kg × (21.3 m/s)² + 0 = 4 kg × 9.8 m/s² × 10 m + 1/2 × 4 kg × (2.8 m/s)² + W₂
0 + 2 kg × 453.69 m²/s² = 392 kgm²/s² + 2 kg × 7.84 m²/s² + W₂
907.38 kgm²/s² = 392 kgm²/s² + 15.68 kgm²/s² + W₂
907.38 kgm²/s² = 407.68 kgm²/s² + W₂
W₂ = 907.38 kgm²/s² - 407.68 kgm²/s²
W₂ = 499.7 kgm²/s²
W₂ = 499.7 J
Since friction is a non-conservative force, the work done by all the non-conservative forces is thus W₂ = 499.7 J
I NEED HELP WITH THIS PLEASE
Answer:
D
Explanation:
One of the factors of increasing the rate of a reaction is increasing concentration. Therefore adding more people increases the number of people on the dance floor , therefore increasing the concentration increases the rate of reaction.
___________________ uses the heat energy from the Earth. This type of alternative energy can be installed basically anywhere in North Carolina.
A) wave energy
B) solar energy
C) nuclear energy
D) geothermal energy
Answer:
Geothermal!!
Explanation:
Geo means earth! Just like Hydro means water, and Pyro means fire :)
Answer:
The Answer is D). Geothermal energy
Explanation:
Hope this helps!!!!!
A 35 kg child slides down a playground slide at a constant speed. The slide has a height of 3.8 m and is 8.0 m long. Find the magnitude of the kinetic friction force acting on the child.
Answer:
The magnitude of the kinetic frictional force acting on the child is 162.93 N
Explanation:
Given;
mass of the child, m = 35 kg
height of the slide, h = 3.8 m
length of the slide, d = 8.0 m
The change in thermal energy associated with the kinetic frictional force is calculated as follows;
[tex]\Delta E_{th} + \Delta K.E + \Delta U = 0\\\\\Delta E_{th} + (\frac{1}{2} mv_f^2 - \frac{1}{2} mv_i^2) + (mgh_f - mgh_i) =0\\\\since \ the \ speed \ is \ constant, \ v_f = v_i \ and \ \Delta K.E = 0\\\\Also, \ final \ height \ , h _f= 0\\\\\Delta E_{th} - mgh_i = 0\\\\\Delta E_{th} = mgh_i\\\\\Delta E_{th} = 35 \times9.8 \times 3.8\\\\\Delta E_{th} = 1303.4 \ J[/tex]
The magnitude of the kinetic frictional force that produced this thermal energy is calculated from the work done by frictional force;
[tex]\Delta E_{th} = F \times d\\\\F = \frac{\Delta E_{th} }{d} \\\\F = \frac{1303.4}{8} \\\\F = 162.93 \ N[/tex]
Therefore, the magnitude of the kinetic frictional force acting on the child is 162.93 N
Communication satellite use__sent by a transmitting station to transmit signals over long distances A microwaves B polar waves C light D radio waves
D: radio waves
Explanation:
radio wves are use to carry satellite signals
An air-filled parallel-plate capacitor has plates of area 2.90 cm2 separated by 2.50 mm. The capacitor is connected to a(n) 18.0 V battery.
Complete question:
An air-filled parallel-plate capacitor has plates of area 2.90 cm2 separated by 2.50 mm. The capacitor is connected to a(n) 18.0 V battery. Find the value of its capacitance.
Answer:
The value of its capacitance is 1.027 x 10⁻¹² F
Explanation:
Given;
area of the plate, A = 2.9 cm² = 2.9 x 10⁻⁴ m²
separation distance of the plates, d = 2.5 mm = 2.5 x 10⁻³ m
voltage of the battery, V = 18 V
The value of its capacitance is calculated as;
[tex]C = \frac{k\epsilon_0A}{d} \\\\C = \frac{(1)(8.85\times 10^{-12})(2.9 \times 10^{-4})}{2.5 \times 10^{-3}} \\\\C = 1.027 \times 10^{-12} \ F[/tex]
Therefore, the value of its capacitance is 1.027 x 10⁻¹² F
A 45.00 kg person in a 43.00 kg cart is coasting with a speed of 19 m/s before it goes up a hill. there is no friction, what is the maximum vertical height the person in the cart can reach?
Answer:
the maximum vertical height the person in the cart can reach is 18.42 m
Explanation:
Given;
mass of the person in cart, m₁ = 45 kg
mass of the cart, m₂ = 43 kg
acceleration due to gravity, g = 9.8 m/s²
final speed of the cart before it goes up the hill, v = 19 m/s
Apply the principle of conservation of energy;
[tex]mgh_{max} = \frac{1}{2}mv^2_{max}\\\\ gh_{max} = \frac{1}{2}v^2_{max}\\\\h_{max} = \frac{v^2_{max}}{2g} \\\\h_{max} =\frac{(19)^2}{2\times 9.8} \\\\h_{max} = 18.42 \ m[/tex]
Therefore, the maximum vertical height the person in the cart can reach is 18.42 m
figure 2. sketch of bar and magnetic field lines observations PLEASE HELPPPP
Lighting is the movement of?
Explanation:
Movement:refers to the changing in the lights whether it be a change in intensity, color or direction of origin.
PLEASE HELP ME WITH THIS ONE QUESTION
Answer:
[tex]^{214} _{83} Bi[/tex] → [tex]^{210}_{81}Tl[/tex] + [tex]^4_2He[/tex]
Explanation:
[tex]^{214} _{83} Bi[/tex] → [tex]x[/tex] + [tex]^4_2He[/tex]
Subtract the [tex]^4_2He[/tex] from the [tex]^{214} _{83} Bi[/tex]
214 - 4 = 210
83 -2 = 81
Therefore, [tex]x[/tex] = [tex]^{210}_{81}Tl[/tex]
who is corazon aquino?
Answer:
Maria Corazon Sumulong Cojuangco Aquino, popularly known as Cory Aquino, was a Filipino politician who served as the 11th President of the Philippines, the first woman to hold that office.
Answer:
Former President of the Philippines
Explanation:
how much heat energy is required to vaporize a 1 g ice cube at 0 C. The heat of fusion of ice is 3.36 x 10^5 J/kg . The heat of vaporization of water is 2.26 x 10^6 J/Kg. ( specific heat of water = 4200 J/Kg C )
Answer:
Q = M * (Cf + C * 100 + Cv)
Cf and Cf are heats of fusion and vaporization and C is the heat required to heat mass M of water 1 deg
Q = .001 kg ( 3.36 * E5 + 100 deg * 4200 + 2.26 * E6) J
Q = .001 kg ( 3.36 J / kg + 4.2 J / kg + 22.6 J /kg) * 10E5
Q = .001 kg * 30.2 * 10E5 J / kg = 3020 J
PLEASE HELP ME WITH THIS ONE QUESTION
The color orange has a wavelength of 590 nm. What is the energy of an orange photon? (h = 6.626 x 10^-19, 1 eV = 1.6 x 10^-19 J)
A) 2.81 eV
B) 3.89 eV
C) 2.10 eV
D) 2.78 eV
k = [tex] \dfrac{ (\dfrac{h}{ \lambda} )^{2} }{2m} [/tex]
k = (6.626×10-¹⁹/590 × 10-⁹ )^{2} /2 × 1.673 × 10-²⁷
k = (1.12 × 10-³⁰)^2/3.346×10-²⁷
k = 1.25 × 10-⁶⁰ /3.346×10-²⁷
k = 0
ldk why, my answer is coming this :(
an object is 70 um long and 47.66um wide. how long and wide is the object in km?
Answer:
length = 7*10^(-8)km
width = 4.666*10^(-8) km
Explanation:
We know that:
1 μm = 1*10^(-6) m
and
1km = 1*10^3 m
or
1m = 1*10^(-3) km
if we replace the meter in the first equation, we get:
1 μm = 1*10^(-6)*1*10^(-3) km
1 μm = 1*10^(-6 - 3)km
1 μm = 1*10^(-9)km
Now with this relationship we can transform our measures:
Length: 70 μm is 70 times 1*10^(-9)km, or:
L = 70*1*10^(-9)km = 7*10^(-8)km
And for width, we have 47.66um, this is 46.66 times 1*10^(-9)km, or:
W = 46.66*1*10^(-9)km = 4.666*10^(-8) km
Select the correct answer.
What happens when two polarizers are placed in a straight line, one behind the other?
A.
They allow light to pass only if they are polarized in exactly the same direction.
B.
They block all light if they are polarized in exactly the same direction.
C.
They allow light to pass only if their directions of polarizations are exactly 90° apart.
D.
They block all light if their directions of polarizations are exactly 90° apart.
E.
They block all light if their directions of polarizations are either exactly the same or exactly 90° apart.
Answer:
C. They allow light to pass only if their directions of polarizations are exactly 90° apart.
Explanation:
If two polarizers are placed in a straight line, one behind the other, they allow light to pass only if their directions of polarizations are exactly 90° apart.
Mention & Instrument used to measure
the mass of the body.
Answer:
a scale is used to measure the mass of the body
A hammer has a mass of 1 kg. What is its weight (i) on Earth (ii) on the
Moon (iii) in outer space
Given mass= 1kg
Weight on earth = mg(gravity of earth) = 9.8N
weight on moon = mg(gravity of moon)= 1.62N
weight on outer space mg(gravity outer space = 0) = 0N
15. Muous produced by snails help them move along the ground How does the mucus help maits
move?
A Mucus is cold
C. Mucus reduces friction
B. Mucus leaves a trail D. Mucus makes the snail lighter
16. Which of the following statements does NOT tell about the effects of pravitational force
on objects?
A. The more distant the body from the earth, the lesser is the gravitational force of attraction
B. Gravitational force pushes the objects upward
C. Gravitational force is greater when the objects are closer together
D. The farther you are from earth, the lesser your weight
17. Why is it difficult for us to go up in a mountain than go down?
A We are moving against gravity
B. We are pulled by the wind
C. We are moving towards gravity
D. None of the above
18. Which of these will have the strongest gravitational pull on Earth'?
A a baby
C. a drinking glass
B. a half sack of nice
D. an elephant
19. Without air resistance, all objects fall at the same rate.
D. Neither True or False
C Maybe
B. False
20. The gravity between two objects increases as the distance between them
D stabilizes
C neutralizes
B. increases
A. decreases
A True
Answer:
15.C Mucus reduces friction
Hot water is added to three times its water at 10 degree Celsius and the resulting temperature at 20 degree Celsius. what is the initial temperature
what are 2 ways that we can express to show our connection to our culture
Answer:
Food, clothes, language, and belief
Who Knows?
Thank You
Answer:
Use below table to read the color codes.
Study the position-time graph for a bicycle. Which statement is supported by the graph? Position vs Time O The bicycle has speed but not velocity. O The bicycle is moving at a constant velocity. O The bicycle has a displacement of 3 m. O The bicycle is not in motion. 3 Position (m) 0 1 2 3 4 5 Time (s) Next Submit Save and Exit Mark this and return tViewers/AssessmentViewer/Activit. 0 M M
Answer:
D) The bicycle is not in motion.
Explanation:
Study the position-time graph for a bicycle.
Which statement is supported by the graph?
A) The bicycle has speed but not velocity.
B) The bicycle is moving at a constant velocity.
C) The bicycle has a displacement of 3 m.
D) The bicycle is not in motion.
Solution:
Velocity is the time rate of change of displacement. It is the ratio of displacement to time taken.
Speed is the time rate of change of distance. It is the ratio of distance to time taken.
From the position-time graph, we can see that the bicycle has a constant positon of 3 m for the whole of the time. That is the position remains 3 m even as the time changes. Therefore, we can conclude that the bicycle is not in motion.
From the position-time data provided, it can concluded that the bicycle is not in motion.
MotionMotion of a body involves a change in the position of that body with time.
A body in motion is constantly changing position or orientation as time passes.
The body may move with constant velocity/speed or changes in its velocity.
A position-time graph provides information about the motion of a body.
From the data provided:
At time 0, the bicycle is at position 3At time 1, the bicycle is at position 3At time 2, the bicycle is at position 3At time 3, the bicycle is at position 3At time 4, the bicycle is at position 3At time 5, the bicycle is at position 3The position of the bicycle remains the same for all time intervals.
Therefore, from the position-time data provided, it can concluded that the bicycle is not in motion.
Learn more about motion and position-time graph at: https://brainly.com/question/2356782
An air-filled pipe is found to have successive harmonics at 700 Hz , 900 Hz , and 1100 Hz . It is unknown whether harmonics below 700 Hz and above 1100 Hz exist in the pipe. What is the length of the pipe
Answer:
the length of the pipe is 0.85 m or 85 cm
Explanation:
Given the data in the question;
The successive harmonics are; 700 Hz , 900 Hz , and 1100 H
Now, for a closed pipe,
length of pipe (L) = λ/4
Harmonics; 1x, 3x, 5x, 7x, 9x, 11x
1100Hz - 900Hz = 200Hz
⇒ 2x = 200Hz
x = 100Hz ( fundamental frequency )
λ = V/f = 340 /100 = 3.4 m
Now
Length L = λ / 4
L = 3.4 / 4
L = 0.85 m or 85 cm
Therefore, the length of the pipe is 0.85 m or 85 cm
A small block, with a mass of 0.05 kg compresses a spring with spring constant 350 N/m a distance of 4 cm. It is released from rest, then slides around the loop and up the incline before momentarily comes to rest at point A. The radius of the loop is 0.1 m.
Required:
Find the elastic potential energy.
Answer:
The elastic potential energy of the spring is 0.28 J
Explanation:
Given;
mass of the block, m = 0.05 kg
spring constant, k = 350 N/m
extension of the spring, x = 4 cm = 0.04 m
The elastic potential energy of the spring is calculated as;
[tex]U_x = \frac{1}{2}kx^2\\\\U_x = \frac{1}{2} \times 350 \times (0.04)^2\\\\U_x = 0.28 \ J[/tex]
Therefore, the elastic potential energy of the spring is 0.28 J