Question

A projectile is to be launched at an angle ${45}^{\circ }$ so that it falls beyond the pond of length $13.6$ $\text{m}$ as shown in the figure and distance between both the points $O$ to $P$ and $M$ to $N$ is $6$ $\text{m}$. What is the range of values of initial velocity (in $m/s$) so that the projectile falls between points $M$ and $N$.

• A. $15<u<16$
• B. $14<u<16$
• C. $13<u<16$
• D. $13<u<14$

Answer 1

The correct option is B $14<u<16$

Range, $R=\frac{u^2\sin 2\theta }{g}$
Given, $OM=6.0+13.6=19.6\text{m}$
$ON=6.0+13.6+6.0=25.6\text{m}$
So, $\Rightarrow 19.6<\frac{u^2\sin 2\theta }{g}<25.6$
$\Rightarrow \frac{19.6\text{g}}{\sin 2\theta }<u^2<\frac{25.6\text{g}}{\sin 2\theta }$
$\Rightarrow \sqrt{\frac{19.6\times 10}{\sin 2\left(45\right)}}<u<\sqrt{\frac{25.6\times 10}{\sin 2\left(45\right)}}$
$\Rightarrow \sqrt{196}<u<\sqrt{256}$
$\Rightarrow 14<u<16$