Question

A gun with a muzzle velocity of $500m/s$ shoots a bullet at a bird $50$ m away. To hit the bird, the gun should be aimed ($g=10m/s^2$)

• A. directly towards the bird along the line joining the gun and bird
• B. $10$ cm high above the bird
• C. $5$ cm high above the bird
• D. $5$ cm below the bird

Answer 1

The correct option is C $5$ cm high above the bird

$R=50=\frac{u^{2}sin2\theta }{g}=\frac{(500{)}^2}{g}sin2\theta$

$50=\frac{(500{)}^2}{10}sin2\theta$

$sin2\theta =\frac{1}{500}.$ Since, $sin2\theta$ is very small

$sin2\theta \approx 2\theta \approx \frac{1}{500}$

$\Rightarrow \theta \approx \frac{1}{1000}$

$tan\theta =\frac{x}{R}\approx \theta \approx \frac{1}{1000}$ ($tan=\theta$ for very small $\theta$)

$\Rightarrow x=\frac{50}{1000}m=0.05m$$=5cm$