Question

Assertion :The path followed by one projectile as observed by another projectile is a straight line Reason: The relative velocity between two projectiles at a given place does not change with time.

• A. Both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
• B. Both Assertion and Reason are true, but Reason is not correct explanation of the Assertion.
• C. Assertion is true, but the Reason is false.
• D. Assertion is false, but the Reason is true.

Answer 1

The correct option is A Both Assertion and Reason are true and the Reason is correct explanation of the Assertion.

If two projectiles were projected from horizontal ground with different intial velocities ($u_a$ and $u_b$) and different angles (A and B) then at any time t :
Coordinates of A: $S_A=\left(u_{a}cosA\right)t\hat{i}-\frac{1}{2}g{t}^2\hat{j}$
Coordinates of B: $S_B=\left(u_{b}cosB\right)t\hat{i}-\frac{1}{2}g{t}^2\hat{j}$
Coordinates of A with respect to B: $S_B-S_A=(u_{b}cosB-u_{a}cosA)t\hat{i}-0j$
Now, $u_{b}cosB-u_{a}cosA$ is constant say k
So, $S_B-S_A=kt\hat{i}-0j$ which corresponds to a straight line ($x=kt$) and the corresponding velocities will not change with time.
Therefore, statement A is true and B is correct explanation.