Question

Say,Mr. X runs on a plain land and jumps from a spot in forward direction. Recognise and describe his jumping motion through an equation and make an argument for your answer.

Answer 1

If he jumped at some angle above the horizontal at some velocity, his range and maximum height will be

$$R=\frac{v^2\sin(2\theta)}{g},\\\space\\ H=\frac{v^2\sin^2\theta}{2g}.$$

He will move by a parabolic trajectory because the motion is accelerated in the vertical direction.