Alex and Kelsey are going to determine the height of tall building. Alex went to

Question

Alex and Kelsey are going to determine the height of tall building. Alex went to third floor hallway

and measured the height of the window there to be 4.0 ft. Kelsey will drop a supper ball from the top

of the building such that it will pass by the window. Alex starts a chronometer (stop watch) as soon

as she sees the ball at top of the window, reads the time as the ball passes the bottom of window. She

reads 0.125s for this event, and does not stop the timer. The timer continues to run while the ball hits

the side walk, bounces back and passes by the window again. Alex stops the chronometer as soon as

she sees the ball arriving at bottom of the window. The timer reads 1.125 seconds. Neglecting the air

resistance, what do they calculate for the building height?

Explanation / Answer

firstly consider only the window part

the ball traveses a height of 4 ft in 0.125 s

use v^2 - u^2 = 2as

v^2 - u^2 = 2*32 * 4

v^2 - u^2 = 256

(v+u)(v-u) = 256 -------(a)

v= u+at

v-u = 32*0.125

v-u = 4 ----------(b)

solve a and b

v =34 , u = 30

now consider the top of the bukiding and the bottom of the window

u = 0 at top of building

v = u + at

34 = 0 + 32*t

t =1.0625 seconds

so it takes 1.0625 seconds to reach the bottom of the window

now consider bottom of the window and the floor

time taken to reach the floor and then bounce back = 1.125 - 1.0625 = 0.0625 seconds

time taken to go down will be equal to time taken to come up

so the time taken to reach the floor will be 0.0625/2 = 0.03125 seconds

we have s = ut + 0.5 *a*t+t

here u is the velocity at the bottom of the window

u = 34 ft/s

t= 0.03125 seconds

s = 34*0.03125 +0.5*32*0.03125*0.03125

s=1.078125 ft

height from the top of the building to bottom of the window

s = 0*1.0625 + 0.5*32*1.0625*1.0625

=18.0625 ft

so the toal height = 0.03125 + 18.0625 ft

=18.09375 ft

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