Question

A projectile is launched from point $A$ of the given landscape with a water body as shown in the diagram. The launching angle is $15^{\circ }$. From the following, identify the right initial velocity of the projectile with which it will fall somewhere in between the points $C$ and $D$.(Assume $g=10m/s^2$ )

• A. 21.5 m / s
• B. 22.5 m / s
• C. 19.5 m / s
• D. 24.0 m / s

Answer 1

Answer: (A)

The given situation is shown below:

According to given condition,
range must be greater than $20m$ and less than $24.2m$.
$\Rightarrow 20\le R\le 24.2$
$\Rightarrow 20\le \frac{u^2\sin 2\theta }{g}\le 24.2$
$\Rightarrow 20\le \frac{u^2\times \sin \left(2\times 15^{\circ }\right)}{10}\le 24.2$
$\Rightarrow 200\le u^2\times \frac{1}{2}\le 242$
$\left(\because \sin 30^{\circ }=\frac{1}{2}\right)$
$\Rightarrow 400\le u^2\le 484$
$\Rightarrow 20m/s\le u\le 22m/s$