Question

Two projectiles are subject to the same acceleration. Motion of one projectile as seen from another projectile will always be a:

• A. Parabola
• B. Circle
• C. Straight line
• D. Hyperbola

Hint:

If two bodies have the same acceleration, their relative acceleration is zero and their relative motion is along a straight line.

Answer 1

The Correct Option is C

Concept:
When two bodies move under the same acceleration, their relative acceleration becomes zero.

Step 1: Let the accelerations of two projectiles be same.
Suppose two projectiles have accelerations: \[ \vec{a}_1=\vec{g} \] and \[ \vec{a}_2=\vec{g} \]

Step 2: Find relative acceleration.
The acceleration of projectile 1 with respect to projectile 2 is: \[ \vec{a}_{12}=\vec{a}_1-\vec{a}_2 \] \[ \vec{a}_{12}=\vec{g}-\vec{g} \] \[ \vec{a}_{12}=0 \]

Step 3: Interpret the motion.
If relative acceleration is zero, then the relative velocity remains constant. So, the relative motion is uniform motion in a straight line. \[ \therefore \text{Motion of one projectile with respect to another is a straight line.} \] \[ \therefore \text{Correct Answer is (C)} \]