Question

Assertion :Using only vertical component of velocity of a projectile, time of flight can be calculated but horizontal range cannot be calculated. Reason: Time of flight depends on horizontal component and range depends on vertical component of velocity of projection.

• A. Both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.
• B. Both Assertion and Reason are true, but Reason is not the correct explanation of the Assertion.
• C. Assertion is true, but the Reason is false.
• D. Assertion is false, but the Reason is true.

Answer 1

The correct option is C Assertion is true, but the Reason is false.

$s_y=ut+\frac{1}{2}a{t}^2$

$u=v\sin \theta ,a=-g$

So, $s_y=v\sin \theta t-\frac{1}{2}g{t}^2$

Time of flight is time for motion when vertical displacement becomes zero.
$s_y=0$
$\Rightarrow 0=v\sin \theta t_f-\frac{1}{2}g{t}_f^2$

$T=\frac{2\left(v\sin \theta \right)}{g}$ ; here $t_f=T$

$T=\frac{2\left(v_y\right)}{g}$

Clearly $T$ is independent of $v_x$.