Question

A grass-hopper can jump a maximum horizontal distance of $0.3$ $m$. If it spends negligible time on the ground, it's horizontal component of velocity is $(g=10m{s}^{-2})$

• A. $\frac{3}{2}m/s$
• B. $\sqrt{\frac{3}{2}}m/s$
• C. $3m/s$
• D. $\frac{2}{3}m/s$

Answer 1

The correct option is B $\sqrt{\frac{3}{2}}m/s$

$R_{max}=0.3m=\frac{u^2\sin 2\theta }{g}$
$R_{max}$ will be at $\theta ={45}^0$
$\Rightarrow \frac{u^2}{g}=0.3$ $mt$
$u^2=3m\Rightarrow u=\sqrt{3}$ $m/s$
Horizontal component $=u\cos \theta$
$=\sqrt{3}\sin {45}^0=\sqrt{\frac{3}{2}}$ $m/s$