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

Question

A playground is on the flat roof of a city school, 5.7 m above the street below (see figure). The vertical wall of the building is h = 7.10 m high, forming 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 0 = 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. Find the speed at which the ball was launched. (Give your answer to two decimal places to reduce rounding errors in later parts.) Find the vertical distance by which the ball clears the wall. Find the horizontal distance from the wall to the point on the roof where the ball lands. Your response differs from the correct answer by more than 10%. Double check your calculations.

Explanation / Answer

Given

angle of projection = 53.0o

Horizontal distance travelled to the wall = 24 m

time taken = 2.2 sec

so projectile speed of the ball

   s = ut

   24 = Vcos(53)*2.2

so V = 18.13 m/sec

time taken for the ball to reach at highst vertical point

      0 = Vsin(53) - 9.8*t

    t = 1.48 sec

    so the time taken by the ball from the highest point to the top of the wall is

      total time - higest time = 2.2 - 1.48 se

                                               = 0.72 sec

   vertical spped of the ball at the top of the wall =

        V1 = -9.8*0.72

             = - 7.06 m/sec

        verticcal distance travelled by ball to touch the roof of ground

         = distance abow the wall + hight of the wall

         = 1.03 + 1.4

          = 1.43 m

vertical speed of the wall after traveling a distance of 1.43 m

v2 -u2 = 2as

v2 = 2* 9.8*1.43 + (7.06)2

v = 8.68 m/sec

time taken for this vertical movment

(v- u) = at

8.68 - 7.06 = 9.8*t

t = 0.1652 sec

Distance travelled in the same time in Horizontal direction =

          s = 18.13*Cos(53)*0.1652

             = 1.80 m

So the answer of Part (c) should be 1.80 m

     

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