Question

A grasshopper can jump a maximum distance $1.6m$. It spends negligible time on the ground. How far can it go in $10s$?
(Take $g=10m/s^2$)

• A. $5\sqrt{2}m$
• B. $10\sqrt{2}m$
• C. $20\sqrt{2}m$
• D. $40\sqrt{2}m$

Answer 1

The correct option is C $20\sqrt{2}m$

Angle of projection = ${45}^{\circ }$ $(\because$ range is maximum at ${45}^{\circ }$
$R_{max}=1.6=\frac{u^2}{g}=\frac{u^2}{10}\text{or}u=4m{s}^{-1}$
Hence, the distance covered in $10s$
$=\text{Horizontal speed}\times \text{time}=u\cos {45}^o\times \text{time}$
$=4\times \frac{1}{\sqrt{2}}\times 10=20\sqrt{2}m$