A shell is fired vertically upwards with a velocity v_1 from a tr… - Vidyadip

MCQ

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
$\frac{2 v_2^2}{g}$
✓
$\frac{2 v_1 v_2}{g}$

✓

Answer

Correct option: D.

$\frac{2 v_1 v_2}{g}$

d
(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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