Question

An aircraft moving with a speed of $1000 \,km/h$ is at a height of $6000 \,m$, just overhead of an anti-aircraft gun. If the muzzle velocity of the gun is $540 \,m/s$, the firing angle $\theta$ for the bullet to hit the aircraft should be

• A. $73^{\circ}$
• B. $30^{\circ}$
• C. $60^{\circ}$
• D. $45^{\circ}$

Answer 1

Answer: (C)

Displacement of aircraft in time t = horizontal displacement of projectile
$\Rightarrow 972\times \frac{5}{18}t =V_{0}\,cos\,\theta \cdot\,t$
$\Rightarrow cos\,\theta = \frac{54 \times 5}{540} =\frac{1}{2}$
$\Rightarrow \theta=60^{\circ}$