Question

A ball is thrown with a velocity of 35 meters per second at an angle of 30° above the horizontal. which quantity has a magnitude of zero when the ball is at the highest point in its trajectory?

Answer 1

The quantity that has a magnitude of zero when the ball is at the highest point in its trajectory is the vertical velocity.

In fact, the motion of the ball consists of two separate motions:
- the horizontal motion, on the x-axis, which is a uniform motion with constant velocity $v_x=v_0 cos 30^{\circ}$, where $v_0=35 m/s$
- the vertical motion, on the y-axis, which is a uniformly accelerated motion with constant acceleration $g=9.81 m/s^2$ directed downwards, and with initial velocity $v_y=v_= sin 30^{\circ}$. Due to the presence of the acceleration g on the vertical direction (pointing in the opposite direction of the initial vertical velocity), the vertical velocity of the ball decreases as it goes higher, up to a point where it becomes zero and it reverses its direction: when the vertical velocity becomes zero, the ball has reached its maximum height.