A playground is on the flat roof of a city school, 6.1 m above the street below

Question

A playground is on the flat roof of a city school, 6.1 m above the street below (see figure). The vertical wall of the building is h =7.50 m high, to form a 1.4-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

A playground is on the flat roof of a city school, 6.1 m above the street below (see figure). The vertical wall of the building is h =7.50 m high, to form a 1.4-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 ? = 53.0degree above the horizontal at a point d = 24.0 m from the base of the building wall. The ball takes 2.20 s to reach a point vertically above the wall.

Explanation / Answer

a) x dirextion

x = v cos theta t
24 = v*cos(53 degrees)*2.2

v=18.13 m/s

b) y = y0 + v0y t + 1/2 a t^2

y = 0 + 18.13*sin(53 degrees)*2.2 - 0.5*9.81*2.2^2=8.11 m

so clears by 8.11 - 7.5 = 0.61 m

c) find time to land

7.5-1.4 = 0 + 18.13*sin(53 degrees)*t - 0.5*9.81*t^2

t=2.44 s

x= 18.13*cos(53 degrees)*2.44 - 24=2.62 m

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