Question

Take the z axis as vertical and the xy plane as horizontal. A particle A is projected at $4\sqrt{2}$ m/s at an angle of ${45}^{\circ }$ to the horizontal, in the xz plane. Particle B is projected at 5 m/s at an angle $\theta =ta{n}^{-1}\left(\frac{4}{3}\right)$ to y axis, in the yz plane. Which of the following is not correct for the velocity of B with respect to A?

• A. Its initial magnitude is 5 m/s.
• B. Its magnitude will change with time.
• C. It lies in the xy plane.
• D. It will initially make an angle $(\theta +\frac{\pi }{2})$ with the positive x axis.

Answer 1

The correct option is B

Its magnitude will change with time.

${\overrightarrow{u}}_A=4\hat{i}+4\hat{k}\&{\overrightarrow{u}}_B=3\hat{j}+4\hat{k}$

${\overrightarrow{v}}_A=(4\hat{i}+4\hat{k})-\left(10t\right)\hat{k}\&\overrightarrow{B}=(3\hat{j}+4\hat{k})-\left(10t\right)\hat{k}$

${\overrightarrow{u}}_{BA}=-4\hat{i}+3\hat{j}\&|{\overrightarrow{u}}_{BA}|=5m/s$

${\overrightarrow{v}}_{BA}=-4\hat{i}+3\hat{j}=-4\hat{i}+3\hat{j}\to$ independent of time