Question

A ball is thrown with an initial speed vi at an angle i with the horizontal. The horizontal range of the ball is R, and the ball reaches a maximum height R/6. In terms of R and g, find: (a) the time the ball is in motion

(b) the ball’s speed at the peak of its path
(c) the initial vertical component of its velocity

Answer 1

(a) The time the ball is in motion is equal to the total time taken to reach its maximum height, plus the time taken to travel the horizontal range, which is given by:

t = (2vi*sin(i))/g + (R)/(vi*cos(i))

(b) The speed of the ball at its peak is given by:

V_peak = √(2g(-R/6))

(c) The initial vertical component of the ball's velocity is equal to vi*sin(i).