Question

A tank moves uniformly along $x$-axis. It fires a shot from origin at an angle of ${30}^{\circ }$ with horizontal while moving along positive $x$-axis and the second shot is also fired similarly except that the tank moves along negative $x$-axis. If the respective range of the shot are $250m$ and $210m$ along $x$-axis, then the speed with which the shot is fired is:

• A. $12m/s$
• B. $53m/s$
• C. $95m/s$
• D. $79m/s$

Answer 1

The correct option is B $53m/s$

range of the projectile is given by (time of flight) *(horizontal velocity)

time of flight will be same as vertical velocity is same in both cases.

let tank is moving with velocity P. and ball is fired with velocity $v$ at angle of 30 degree with horizontal.

then $(vCos30+P)\times \left(\frac{2vSin30}{g}\right)=250$

$(vCos30-P)\times \left(\frac{2vSin30}{g}\right)=210$

adding both equations we get $\left(2vCos30\right)\left(2vsin30\right)=460\times g$

$v^2=2658.959$

$v=53m/s$.