Question

The greatest height to which a man can a stone is $h$. What will be the greatest distance up to which he can throw the stone.

Answer 1

The greatest height to which a man can throw a stone is h.

Now, this height will be achieved when the stone is thrown vertically upwards.

$v^2$= $2gh$. . . . . . . ( 1 )

When the stone is projected at an angle, it reaches a certain maximum distance.

This is called the range of a projectile which is given as:

R = $\frac{v^{2}sin2\theta }{g}$

We knew that the maximum range is attained when $\theta$ = ${45}^{\circ }$

and $sin2\theta$ = 1

R =$\frac{v^2}{g}$

from ( 1 ), we get

$R=\frac{2gh}{g}$ = $2h$

Therefore, if a man can throw a stone to maximum height $h$

then he can throw the same stone to a maximum distance $2h$.