A football player throws a 400 g football at 30 to the horizontal. Being in a go

Question

A football player throws a 400 g football at 30 to the horizontal. Being in a good physical condition, he is able to impart initial kinetic energy of 100 J to the ball. The ball is caught at exactly the same height above the ground as it was thrown.

i. What is the initial speed of the ball (immediately after it has separated from the athlete’s hand)?

ii. What is the vertical component of the ball’s velocity?

iii. How long will it tackle for the ball to get to the maximum height?

iv. How long will it take for the ball to get up to the maximum and then fall back to the initial height?

v. What is the horizontal component of the ball’s initial velocity?

vi. How far will the ball travel in the horizontal direction within the time found in (iv)?

Explanation / Answer

i) initial kinetic energy, (1/2)mv2 = 100 J

or 0.5*0.4*v2 = 100

or initial speed of the ball (immediately after it has separated from the athlete’s hand, v = 22.36 m/s

ii) vertical component of the ball’s velocity, vv = vsin30o = 22.36/2 = 11.18 m/s

iii) time taken by the ball to get to the maximum height , t = vv/g = 11.18/9.81 = 1.14 s

iv) time taken by the ball to get up to the maximum and then fall back to the initial height, T = 2t = 2.28 s

v) horizontal component of the ball’s initial velocity, vh = vcos30o = 19.36 m/s

vi) distance travelled by ball in the horizontal direction within the time T, d= vh*T = 19.36*2.28 m = 44.14 m

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