Question

Two particles at $t=0$ are thrown horizontally in opposite directions from the same point from a height $h$ with velocities $4m{s}^{-1}$ and $3m{s}^{-1}$. Find the time when their velocities are perpendicular.

• A. $0.15s$
• B. $0.25s$
• C. $0.35s$
• D. none of these

Answer 1

Answer: (C)

$0.35s$

$\overrightarrow{V_1}=-4\hat{i}-gt\hat{j}$ and $\overrightarrow{V_2}=3\hat{i}-gt\hat{j}$ are the velocities at any instant.
For velocities to be perpendicular $\overrightarrow{V_1}.\overrightarrow{V_2}=0$
$\overrightarrow{V_1}.\overrightarrow{V_2}=0$ $⟹t=\sqrt{\frac{12}{g^2}}=0.35s$