Question

A homerun is hit in such a way that the baseball just clears a wall 21m high, located 130m from the home plate. The ball is hit at an angle of 35° to the horizontal, and air resistance is negligible. Find (a) initial speed of the ball, (b) the time it takes the ball to reach the wall, and (c) the velocity components and the speed of the ball when it reaches the wall. (Assume the ball is hit at a height of 1m above the ground)

Answer 1

(a)

$t=x/v_{ix}=130/(v_i\cdot\cos35°)=159/v_i$

At this time, the ball must be $20(m)$ above its launch position.

$y=v_{iy}t+0.5a_yt^2\to$

$20=v_i\sin35°\cdot (159/v_i)-4.9\cdot(159/v_i)^2\to v_i=42(m/s)$

(b)

$t=159/42=3.8(s)$

(c)

$v_x=v_{ix}=42\cdot\cos35°=34(m/s)$

$v_y=v_{iy}+a_yt=42\cdot\sin35°-9.8\cdot3.8=-13(m/s)$

$v=\sqrt{34.1^2+(-13)^2}=37(m/s)$