A ball is thrown from the roof of a building at a speed of 20 m/s and an angle o

Question

A ball is thrown from the roof of a building at a speed of 20 m/s and an angle of 30 degree above the horizontal. It takes the ball 4 seconds to reach the ground. Sketch a motion diagram and a pictorial representation before setting up and solving your kinematics equations. These diagrams are part of your score on this question. How tall is the building? What is the ball's speed and direction as it contacts the ground? How far from the base of the building does the ball land? What maximum height does the ball reach?

Explanation / Answer

vi= 20m/s

vix= 20cos30 = 17.3 m/s

viy=20sin30 = 10.0 m/s

a) h = viy*t -1/2*gt^2 = 10*4 -1/2*9.8*4^2 = - 38.4 m

b) vfx = vix = 17.3 m/s

vfy = viy – gt= 10.0 - 9.8*4 = -29.2 m/s

vf = sqrt(17.3^2 + 29.2^2) = 33.94 m/s

c) x = vix*t = 17.3*4 = 69.4 m

d) At max height , vfy= 0 m/s

vfy^2 = viy^2 -2gHmax

0^2 = 10.0^2 -2*9.8*Hmax

Gives, Hmax = 5.1 m

Total Hmax = 38.4 + 5.1 = 43.5 m

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