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 ....
✓
Answer
(d)
There is no acceleration in the horizontal direction.
$S_x=U_x T+\frac{1}{2} a_0 \times T^2$
$R=U_x T \ldots (1)$
$S_y=U_y T+\frac{1}{2} g_y T^2$
$O=V_1 T-\frac{1}{2} g T^2$
$\Rightarrow V_1 T=\frac{1}{2} g T$
$T=\frac{2 V_1}{g}$
We know,
$(R)$ range $=($ Horizontal velocity $4 x) \times$ flight $+$ time $(T)$
i.e., $R=4 x \times T$
$R=V_2 \times \frac{2 V_1}{g} \Rightarrow \frac{2 V_1 V_2}{g}$
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