Question

A shell is fired vertically upwards with a velocity $v_1$ from a trolley moving horizontally with velocity $v_2$. A person on the ground observes the motion of the shell as a parabola, whose horizontal range is

• A. $\frac{2v_1^2{v}_2}{g}$
• B. $\frac{2v_1^2}{g}$
• C. $\frac{2v_2^2}{g}$
• D. $\frac{2v_1{v}_2}{g}$

Answer 1

Answer: (D)

There is no acceleration in the horizontal direction
$S_x=U_{x}T+\frac{1}{2}{a}_0\times T^2$
$R=U_{x}T$ ...(1)
$S_y=U_{y}T+\frac{1}{2}{g}_y{T}^2$
$O=V_{1}T-\frac{1}{2}g{T}^2$
$\Rightarrow V_{1}T=\frac{1}{2}gT$
$\Rightarrow =\frac{2V_1}{g}$
We know,
$(R)$ range $=($ Horizontal velocity $4x)\times$ flight $+$ time $(T)$
i.e., $R=4x\times T$
$R=V_2\times \frac{2V_1}{g}$
$\Rightarrow \frac{2V_1{V}_2}{g}$