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. $\frac{2 v_{1}^{2} v_{2}}{g}$
• B. $\frac{2 v_{1}^{2}}{g}$
• C. $\frac{2 v_{2}^{2}}{g}$
• D. $\frac{2 v_{1} v_{2}}{g}$

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)
$S_{y}=U_{y} T+\frac{1}{2} g_{y} T^{2}$
$O=V_{1} T-\frac{1}{2} g T^{2}$
$\Rightarrow V_{1} T=\frac{1}{2} g T$
$\Rightarrow =\frac{2 V_{1}}{g}$
We know,
$(R)$ range $=($ Horizontal velocity $4 x) \times$ flight $+$ time $(T)$
i.e., $R=4 x \times T$
$R=V_{2} \times \frac{2 V_{1}}{g}$
$\Rightarrow \frac{2 V_{1} V_{2}}{g}$