A shell is fired vertically upwards with a velocity v₁ from a trolley moving horizontally with vel

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3-2.Motion in Plane

hard

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

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

Solution

(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., $R=4 x \times T$

$R=V_2 \times \frac{2 V_1}{g} \Rightarrow \frac{2 V_1 V_2}{g}$

Standard 11

Physics

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