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 $g=10\, m / s ^{2}$ )

• 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 $20 \,m$ and less than $24.2 \,m$.
$\Rightarrow 20 \leq R \leq 24.2$
$\Rightarrow 20 \leq \frac{u^{2} \sin 2 \theta}{g} \leq 24.2$
$\Rightarrow 20 \leq \frac{u^{2} \times \sin \left(2 \times 15^{\circ}\right)}{10} \leq 24.2$
$\Rightarrow 200 \leq u^{2} \times \frac{1}{2} \leq 242$
$ \left(\because \sin 30^{\circ}=\frac{1}{2}\right)$
$\Rightarrow 400 \leq u^{2} \leq 484$
$ \Rightarrow 20 \,m / s \leq u \leq 22\, m / s$