A playground is on a flat roof of a city school, 5.7m above the street below. Th

Question

A playground is on a flat roof of a city school, 5.7m above the street below. The wall of the building is h=6.9m high, forming a 1.2m 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 degrees above the horizontal at a point d=24m from the base of the building wall. The ball takes 2.20s to reach the point vertically above the wall. a) Find the speed at which the ball is launched. b) Find the vertical distance by which the ball clears the wall. c) Find the distance from the wall to the point on the roof where the ball lands.

Explanation / Answer

a) x = v0*cos(theta)*t

vo = 24/cos(53)*2.2

v0 = 18.18 m/s

b) y = v0sin53*t-1/2gt^2

y = 18.18sin53*2.2-4.9*2.2^2

y = 8.23 m

h = 8.23-6.9 = 1.33 m

c) y' = vosin53*t-1/2gt^2

4.9t^2-18.18sin53*t+5.7 = 0

t = 2.49 sec

vocos53*t = 24+d

d = 3.24 m

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