Question

A gray hopper can jump a maximum horizontal distance of 0.3 m. If it spends negligible time on ground, its horizontal component of velocity

• A. $\frac{3}{2}m/s$
• B. $\sqrt{\frac{3}{2}}m/s$
• C. $\frac{1}{2}m/s$
• D. none of these

Answer 1

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

As it spend negligible time on ground so its motion can be considered as that of a $projectile$.Maximum horizontal range for a projectile is $R=\frac{u^{2}Sin2\theta }{g}$, with $\theta ={45}^0$

so $0.3=\frac{u^2\times 1}{10}$ so $u^2=3$ or $u=\sqrt{3}m/s$

$u$ is the projection velocity.

So the horizontal component of velocity will be $uCos{45}^0=\sqrt{\frac{3}{2}}m/s$