Question

A tank moves uniformly along x-axis. It fires a shot from origin at an angle of ${30}^0$ 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 $200m$ along x-axis,the velocity of tank is

• A. $3.9m{s}^{-1}$
• B. $4.9m{s}^{-1}$
• C. $5.9m{s}^{-1}$
• D. $9.4m{s}^{-1}$

Answer 1

The correct option is B $4.9m{s}^{-1}$

In both the cases vertical component of projection will remain the same i.e $u\sin \theta$(as there is no vertical motion of the tank), therefor Time of flight will be same in both the cases.
Only horizontal component of the shell will be different with respect to ground
in first case it will be $V+u\cos \theta$ and in the second case it will be $V-u\cos \theta$
so Range R = Horizontal speed * Time-of-flight
hence we can write
$\frac{V+u\cos \theta }{V-u\cos \theta }=\frac{250}{200}$ .......(1)
also
$(V+u\cos \theta )\frac{2u\sin \theta }{g}=250$ ........(2)
on solving two equations (1) and (2) we get
$V=4.9m/s$