Question

A gun moving at a speed of $30m/s$ fires a bullet (in the same direction gun is moving) at an angle ${30}^o$ with the horizontal and a velocity of $150m/s$ relative to the gun. Find the distance between the gun and the bullet when the bullet hits the ground. (Take $g=10m/s^2$)

• A. $1500m$
• B. $2400m$
• C. $1950m$
• D. $1000m$

Answer 1

The correct option is C $1950m$

Vertical component of velocity of the bullet relative to gun = $V_{by}=150\sin {30}^{\circ }=75m/s$
Horizontal component of velocity of bullet relative to gun = $V_{bx}=150\cos {30}^{\circ }=75\sqrt{3}m/s$
Horizontal component of velocity of bullet relative to ground, $v_b=75\sqrt{3}+30\approx 160m/s$
Time of flight $t=\frac{2v_b\sin \theta }{g}=\frac{(2\times 75)}{10}=15s$
Range of projectile $R=160\times 15=2400m$
Distance moved by the gun $=30\times 15=450m$
Distance between the gun and the projectile $=2400-450=1950m$
Hence the correct option is (c).