How would I solve this question? \" A ball is dropped from the top of an apartme

Question

How would I solve this question?

" A ball is dropped from the top of an apartment building. A person is on a patio somewhere beneath the top of the apartment building and the person notices the ball takes 0.15 seconds to fall from the top of his patio to the bottom of his patio. The height of his patio is 3 meters. If the bottom of the person's patio is 57.9 meters from the ground, or bottom of the building, how high, in meters, is the apartment building? Hint: you must find how far above the top of the patio the ball was dropped and then use that with the other given information related to the heights to find the height of the building."

Explanation / Answer

let vy is the speed of the ball at the top of the patio.

let height of the pation, h = 3m

now use kinematic equation,

distance travelled in 0.15 s,
h = vy*t + 0.5*g*t^2

3 = vy*0.15 + 0.5*9.8*0.15^2

3 = 0.15*vy + 0.11

==> vy = (3 - 0.11)/0.15

= 19.27 m/s

initail veloicty of the ball, voy = 0

let d is the distance from top of the building to top of the patio.

so, we can write

vy^2 - voy^2 = 2*g*d

vy^2 - 0 = 2*g*d

==> d = vy^2/(2*g)

= 19.26^2/(2*9.8)

= 18.94 m

so, total height of the building = 18.94 + 3 + 57.9

= 79.84 <<<<<<<<<----------------Answer

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