Question

Trajectories are shown in figure for three kicked footballs. Initial vertical & horizontal velocity components are $u_y$ and $u_x$ respectively. Ignoring air resistance, choose the correct statement from Column II for the value of variable in Column I.
$\begin{array}{cc}\text{Column I}& \text{Column II}\\ \text{(A) Time of flight}& \text{(P) Greatest for}A\text{only}\\ \text{(B)}{u}_y/u_x& \text{(Q) Greatest for}C\text{only}\\ \text{(C)}{u}_x& \text{(R) Equal for}A\text{and}B\\ \text{(D)}{u}_x{u}_y& \text{(S) Equal for}B\text{and}C\end{array}$

Which of the following option has the correct combination considering column-I and column-II ?

• A. D $\to$ Q
• B. A $\to$ S
• C. C $\to$ R
• D. B $\to$ P

Answer 1

The correct option is D B $\to$ P

[(A) $\to$ R; (B) $\to$ P; (C) $\to$ Q; (D) $\to$ S]

For a projectile motion

$R=\frac{u^2\sin 2\theta }{g},T=\frac{2u\sin \theta }{g},H=\frac{u^2{\sin }^2\theta }{2g}$
(A) If $H_{\text{max}}$ is same for two projectile, time of flight be also same.
(B) $u_y/u_x=\tan \theta$
So, it is greatest when angle is greatest.
(C)
Height of A and B is same, i.e $u_y$ is equal for them.
As Range of B > Range of A, $u_x$ is higher for B.

Range is equal for B and C, so $u_{x}T$ is same for B and C.
As $T$ is higher for B, $u_x$ is highest for C.


(D) $u_x{u}_y=u^2\sin \theta \cos \theta =\left(u^2\sin 2\theta \right)/2$
So, if range is equal then $u_x{u}_y$ is also equal.