Determining the Height of a Building

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SUMMARY

The problem involves determining the height of a building using the time a ball spends in front of a window and the physics of free fall. The ball takes 0.30 seconds to pass the 1.50-meter tall window while falling and again while rising. Given that the ball spends a total of 2.50 seconds below the window, the equations of motion, specifically \(\Delta x = v_{0}t + (1/2)at^{2}\), are utilized to calculate the height of the building. The solution requires finding the distance to the top of the window and the total time for the ball to reach the ground.

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Homework Statement


You are sitting by a window when someone on the roof drops a ball. The ball spends .30 seconds in front of the window (which is 1.50 meters tall.) The ball subsequently hits the sidewalk and bounces back up at the same speed. On its way up it passes by the window again taking .30 seconds in front of the window. If the ball spends 2.50 seconds underneath the window then how tall is the building?


Homework Equations


[itex]\Delta x = v_{0}t+(1/2)at^{2}[/itex]


The Attempt at a Solution


I have absolutely no idea how to approach this problem. I would appreciate any help.
 
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Hint: Try to find the distance d to the top first. After falling an unknown time t (without initial velocity), the ball has fallen a distance of d and reaches the top of the window. 0.3 seconds later the distance of the ball increased by 1.5 m. Try to express that with equations and solve them for d and t.
Afterwards, try to find the total time the ball needs to reach the floor.

You can assume that the building is on earth, so you know the acceleration.
 

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