Question

Assertion :Two projectiles have maximum heights $4H$ and $H$ respectively. The ratio of their horizontal components of velocities should be $1:2$ for their horizontal ranges to be same. Reason: Horizontal range= horizontal component of velocity $\times$ time of flight.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Maximum height is given as $\frac{u^2{\sin }^2\theta }{2g}$, while Time of flight is $\frac{2u\sin \theta }{g}$. Thus, $H\propto T^2$
Thus for given projectile, $T_1:T_2=\sqrt{4}:\sqrt{1}=2:1$
Now, second statement is correct, Horizontal range= horizontal component of velocity X time of flight.
Thus, for range to be same, $u_{x_1}:u_{x_2}=1:2$, because times are in ratio 2:1
Thus 2nd statement explains first also