# A falling stone takes 0.28s to travel past a window 2.2m tall … ?

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A falling stone takes 0.28s to travel past a window 2.2m tall. From what height above the top of the window did the stone fall?

a= -9.80 m/s^2

• Find the velocity of the stone when it reaches the top of the window.

s = u×t + a×t²/2

where

s = displacement = -2.2 m (bottom of window below top, so negative)

u = initial velocity = ?

t = time = 0.28 s

a = acceleration by gravity = -9.8 m/s²

so

-2.2 = u×0.28 + (-9.8)×0.28²/2

u = -6.485 m/s (negative because falling down)

Now find the distance at which it must have started.

v² = u² + 2×a×s

where

v = final velocity = -6.485 m/s

u = initial velocity = 0 m/s

a = acceleration by gravity = -9.8 m/s²

s = displacement = ?

so

(-6.485)² = 0² + 2×(-9.8)×s

s = -2.146 m (negative because final height below initial height)

The stone fell from 2.146 m above the window < – – – – – ANSWER

• You can solve this problem by using the formula s = 1/2 at^2 where s is the total distance travelled a = 9.80 and t = 0.28 seconds.

Solve for s and don’t forget to subtract the height of the window to get the answer

• I made a mistake, here is the correct work.

As the travels past the window, its velocity increases 9.8 m/s each second for 0.28 seconds.

vf = vi + 9.8 * 0.28

vf = vi + 2.744

Use the following equation to determine the velocity of the stone at the top of the window.

vf^2 – vi^2 +(2 * a * d) a = 9.8 m/s^2, d = 2.2 m

2 * a * d = 2 * 9.8 * 2.2 = 43.12

vf^2 = vi^2 + 5.488 * vi + 2.744^2

vf^2 – vi^2 = vi^2 + 5.488 * vi + 2.744^2 – vi^2

vf^2 – vi^2 = 5.488 * vi + 2.744^2

5.488 * vi + 2.744^2 = 43.12

vi = (43.12 – 2.744^2) ÷ 5.488 = 6.485 m/s

This is the velocity at the top of the window.

Velocity at bottom = 6.485 + 0.28 * 9.8 = 9.229 m/s

Check

d = vi * t + ½ * a * t^2 = 6.485 * 0.28 + ½ * 9.8 * 0.28^2 = 2.2 meters

As the stone fell from its initial height to the top of the window, its velocity increased from 0 m/s to 6.485 m/s at the rate of 9.8 m/s each second.

Time = (vf – vi) / a = (6.485 – 0) / 9.8 = 6.485/9.8

d = vi * t + ½ * a * t^2, vi = 0 m/s

d = ½ * 9.8 * (6.485/9.8)^2 = 2.15 meters

The total distance the stone fell = 2.15 + 2.2 = 4.35 m meters

This is the initial height of the stone.

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