A stone is dropped off the science building and accelerates, from rest, toward the ground at 9.8 m/s/s. A curious physics student looks out the third floor window as the stone falls past. She happens to have a stopwatch and she finds that it takes 0.30 sec for the stone to fall past the 2.2 m tall window. She then sketches the velocity vs. time plot shown below, but realizing she is late for lunch, she doesn't use the plot to analyze the motion of the stone.

Question

A stone is dropped off the science building and accelerates, from rest, toward the ground at 9.8 m/s/s. A curious physics student looks out the third floor window as the stone falls past. She happens to have a stopwatch and she finds that it takes 0.30 sec for the stone to fall past the 2.2 m tall window. She then sketches the velocity vs. time plot shown below, but realizing she is late for lunch, she doesn't use the plot to analyze the motion of the stone.

A) WHat was the average velocity of the stone as it fell past the window?

B) What was the velocity of the stone at the top of the window?

C) From what height above the top of the window did the stone start its fall?

Answer 1

average velocity= 2.2/.3 m/s

So, if the average velocity is that, that is the velocity at the center. What is the velocity at the top of the window?

Vf=Vi-gt
Vf(at top)=-2.2/.3-9.8(-.15) where t is before the center, at t=-.15
Vf you calculate.
Height?
Vf(top of window)^2=2*g*d
solve for distance d.

Answer 2

i still don't understand how to do parts b and c.

Answer 3

To answer these questions, we need to use the information given and apply relevant physics formulas. Let's break it down step by step:

A) To find the average velocity of the stone as it fell past the window, we can use the formula:
Average Velocity = Change in displacement / Change in time

In this case, the change in displacement is the height of the window (2.2 m) and the change in time is the time it takes for the stone to fall past the window (0.30 sec).

Average Velocity = 2.2 m / 0.30 sec = 7.33 m/s

So, the average velocity of the stone as it fell past the window is 7.33 m/s.

B) To find the velocity of the stone at the top of the window, we can use the formula for final velocity in uniformly accelerated motion:
Final Velocity = Initial Velocity + (Acceleration * Time)

Here, the initial velocity of the stone is 0 m/s (as it starts from rest), the acceleration is the acceleration due to gravity (-9.8 m/s^2), and the time is the time it takes to fall past the window (0.30 sec).

Final Velocity = 0 m/s + (-9.8 m/s^2) * 0.30 sec = -2.94 m/s

The negative sign indicates the downward direction, so the velocity of the stone at the top of the window is -2.94 m/s.

C) Finally, to find the height from which the stone started its fall, we can use the formula for the displacement in uniformly accelerated motion:
Displacement = Initial Velocity * Time + (0.5 * Acceleration * Time^2)

Here, the initial velocity is 0 m/s, the acceleration is -9.8 m/s^2, and the time is the time it takes to fall past the window (0.30 sec).

Displacement = 0 m/s * 0.30 sec + (0.5 * -9.8 m/s^2 * (0.30 sec)^2)

Displacement = -0.44 m

So, the stone started its fall from a height of 0.44 m above the top of the window.

In summary:
A) The average velocity of the stone as it fell past the window is 7.33 m/s.
B) The velocity of the stone at the top of the window is -2.94 m/s.
C) The stone started its fall from a height of 0.44 m above the top of the window.