Suppose the ball is thrown at the same initial speed but at

Question

A ball is thrown with an initial speed v_i at an angle θ_i with the horizontal. The horizontal range of the ball is R, and the ball reaches a maximum height R/4. In terms of R and g, find the following.

(a) the time interval during which the ball is in motion

t=   

(b) the ball's speed at the peak of its path

v=   

(c) the initial vertical component of its velocity

y_i=   

(d) its initial speed

v_i=   

(e) the angle θ_i

θ_i=   

(f) Suppose the ball is thrown at the same initial speed found in (d) but at the angle appropriate for reaching the greatest height that it can. Find this height.

h_max=   

(g) Suppose the ball is thrown at the same initial speed but at the angle for greatest possible range. Find this maximum horizontal range.

x_max=