Question

A grass hopper can jump maximum distance for a jump height of $1.6m$. It spends negligible time on ground. How far can it go in $\frac{10}{\sqrt{2}}$s?

• A. $45m$
• B. $30m$
• C. $20m$
• D. $40m$

Answer 1

Answer: (D)

$40m$

Maximum distance will be for 45 degree angle of jump. Given maximum height $=1.6m=\frac{u^{2}si{n}^2{45}^0}{2g}$ Thus, $u=\sqrt{40\times 1.6}=8m/s$.
Thus, maximum horizontal distance will be $\frac{u^{2}sin2\theta }{g}=\frac{64}{10}=6.4m$ which is covered in time $t=\frac{2u\sin \theta }{g}=\frac{16}{10\sqrt{2}}=0.8\sqrt{2}$
Thus, in $10/\sqrt{2}$ seconds, distance covered=$\frac{6.4\times 10}{0.8\times 2}=40m$