Question

A ball is batted into the air and caught at a point 100 m distance horizontally in 4.0 seconds. Neglecting air resistance. Find the maximum height attain by the ba

Answer 1

The height of the ball batted at some angle depends on its initial velocity and the angle:

$$h=\frac{v^2\text{sin}^2\theta}{2g}.$$

The time of flight is

$$t=\frac{2v\text{ sin}\theta}{g},\\\space\\ v\text{ sin}\theta=\frac{gt}{2}.$$

Thus, the maximum height is (we substitute the right part of the last equation above)

$$h=\frac{(gt/2)^2}{2g}=\frac{gt^2}{8}=19.6\text{ m}.$$