Two particles are simultaneously projected in opposite directions… - Vidyadip

MCQ

Two particles are simultaneously projected in opposite directions horizontally from a given point in space, where gravity $g$ is uniform. If $u_1$ and $u_2$ be their initial speeds, then the time $t$ after which their velocities are mutually perpendicular is given by

✓
$\frac{\sqrt{u_1 u_2}}{g}$
B
$\frac{\sqrt{u_1^2+u_2^2}}{g}$
C
$\frac{\sqrt{u_1\left(u_1+u_2\right)}}{g}$
D
$\frac{\sqrt{u_2\left(u_1+u_2\right)}}{g}$

✓

Answer

Correct option: A.

$\frac{\sqrt{u_1 u_2}}{g}$

a
(a)

$v _1 \perp v _2$

$\therefore \quad v _1 \cdot v _2=0$

$\text { or }\left(u_1 \hat{ i }-g t \hat{ j }\right) \cdot\left(-u_2 \hat{ i }-g t \hat{ j }\right)=0$

$\therefore \quad g^2 t^2=u_1 u_2$

$\text { or }$

$t=\frac{\sqrt{u_1 u_2}}{g}$

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