Question

A grasshopper can jump upto a height h. Find the maximum distance through which it can jump along the horizontal ground.

Answer 1

The grasshopper can jump upto a height h. It means the maximum possible height it can achieve, i.e., when it jumps vertically.
Since $h=\frac{v^{2}si{n}^2\theta }{2g}$, when $\theta ={90}^o$,
$h=\frac{v^2}{2g}\Rightarrow v^2=2gh$ ...(i)
Now, maximum range, $\frac{v^2}{g}=\frac{2gh}{g}=2h\Rightarrow R=2h$