A playground is on the flat roof of a city school, 7.00 m above the street below

Question

A playground is on the flat roof of a city school, 7.00 m above the street below. The vertical wall of the building is 8.00 m high, forming a 1.00 m high railing around the playground. A ball has fallen to the street below, and a passerby returns it by launching it at an angle of 53.0 above the horizontal at a point 27.0 m from the base of the building wall. The ball takes 2.20 s to reach a point vertically above the wall.
(a) Find the speed at which the ball was launched.
_____m/s

(b) Find the vertical distance by which the ball clears the wall.
_____m

(c) Find the distance from the wall to the point on the roof where the ball lands.
_____m

Explanation / Answer

a)

vx = d/t = 27/2.2 = 12.273 m/s

v = vx/cos = 12.273/cos53 = 20.393 = 20.4 m/s

b)

H = -0.5 g t^2 + v sin t = -0.5*9.8*2.2*2.2 + 20.393*2.2*0.798636 = 12.114 m

h' = 12.114 - 8 = 4.1145 = 4.11 m

c)

H' = 4.1145 + 1 = 5.1145 m

v'y = vy - g t = 20.393*0.798636 - 9.81*2.2 = -5.2954 m/s

H' = -0.5 g t^2 + v'y t

-5.1145 = -0.5*9.8*t^2 - 5.2954 t

>>> t = 0.6154 s

>>> d' = 0.6154 * 12.273 = 7.55 m

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