Question

A projectile is thrown with an initial velocity $(a \hat{i}+b \hat{j}) m / s ,$ where $\hat{i}$ and $\hat{j}$ are the unit vectors along horizontal and vertical directions respectively. If the range of projectile is twice the maximum height reached by it, then

• A. $b=\frac{a}{2}$
• B. $b=a$
• C. $b=2 a$
• D. $b=4 a$

Answer 1

Answer: (C)

Given initial velocity, $\vec{u}=a \hat{i}+b \hat{j}$
$\therefore u_{x}=a, u_{y}=b$
Time of flight, $T=\frac{2 u_{y}}{g}=\frac{2 b}{g}$
Maximum height, $H=\frac{u_{y}^{2}}{2 g}=\frac{b^{2}}{2 g}$
Range, $R=\frac{2 u_{x} u_{y}}{g}=\frac{2 a b}{g}$
$\because R=2 H$ (Given)
$\therefore \frac{2 a b}{g}=2 \times \frac{b^{2}}{2 g} $
or $ 2 a=b$