Atennis ball is thrown from ground level with velocity directed 30° above the horizontal. if it takes the ball 0.5 s to reach the top of its trajectory, what is the magnitude of the initial velocity?

The motion of the tennis ball on the vertical axis is an uniformly accelerated motion, with deceleration of  (gravitational acceleration).

The component of the velocity on the y-axis is given by the following law:

At the time t=0.5 s, the ball reaches its maximum height, and when this happens, the vertical velocity is zero (because it is a parabolic motion): . Substituing into the previous equation, we find the initial value of the vertical component of the velocity:


However, this is not the final answer. In fact, the ball starts its trajectory with an angle of . This means that the vertical component of the initial velocity is

We found before , so we can substitute to find , the initial speed of the ball:

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