Question

Projectile A is thrown horizontaly from tower of height H and projectile B is thrown from the ground at an angle $\theta$ as shown in the figure. During the duration when both are in air,

• A. Path of A as seen by B will be a straight line
• B. Path of A as seen by B will be a parabola
• C. Motion of A is uniformly accelerated as seen by B.
• D. Relative acceleration of A with respect to B is zero

Answer 1

Answer: (A), (D)

Relative acceleration of A with respect to B is zero

Say,
rightside is positive x axis and
upwards is positive y axis.
$V_{AB}$ is velocity of A w.r.t. B.
${\overrightarrow{V}}_{AB}={\overrightarrow{V}}_A-{\overrightarrow{V}}_B\Rightarrow$
${\overrightarrow{V}}_A={\overrightarrow{V}}_{OA}-\overrightarrow{g}t=V_{OA}\hat{i}-gt\hat{j}$ .....(1)
$V_B={\overrightarrow{V}}_{OB}-\overrightarrow{g}t=V_{OB}cos\theta \hat{i}+V_{OB}sin\theta \hat{j}-gt\hat{j}$ ....(2)
${\overrightarrow{V}}_{AB}=(V_{OA}-V_{OB}cos\theta )\hat{i}-V_{OB}sin\theta \hat{j}$
as we can see ${\overrightarrow{V}}_{AB}$ is constant, and the relative acceleration between the bodies is zero. This implies, the path of the body is a straight line.