Question

A baseball is thrown horizontally with an initial velocity of 20m/s from the height of 1.5m. How long will it take to reach the ground? How far will it go horizontally?

Answer 1

Equations of motion of baseball are $y(t) = h - \frac{g t^2}{2}$, $x(t) = v_0 t$, where $h$ is the initial height, and $v_0$ is the initial horizontal velocity.

When the ball reaches the ground, $y(t) = 0$, from where it takes $t_1 = \sqrt{\frac{2 h}{g}} \approx 0.55 s$ to reach the ground.

Substituting the time $t_1$ from the last equation into equation for $x(t)$, obtain the horizontal distance covered: $s = x(t_1) = v_0 \sqrt{\frac{2 h}{g}} \approx 11.06 m$