Question

Two small bodies of different masses are projected upwards with the same velocity but making angle of projection of \(30^{\circ }\) and \(60^{\circ }\) with the horizontal. Both these bodies will

• A. attain the same height.
• B. have the same time of flight.
• C. have same trajectory.
• D. have the same horizontal range

Hint:

The range of a projectile is the same for angles of projection that are complementary.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
The horizontal range is \(R=\dfrac{u^{2}\sin 2\theta}{g}\). It does not depend on the mass of the body.

Step 2: Calculation
For \(30^{\circ}\): \(\sin 60^{\circ}=\dfrac{\sqrt{3}}{2}\). For \(60^{\circ}\): \(\sin 120^{\circ}=\dfrac{\sqrt{3}}{2}\).
So both ranges are equal.

Step 3: Check the other statements
Maximum height \(\dfrac{u^{2}\sin^{2}\theta}{2g}\) and time of flight \(\dfrac{2u\sin\theta}{g}\) differ for the two angles, so the trajectories also differ.

Final Answer:
Both bodies have the same horizontal range. \[ \boxed{\text{(D) }\text{have the same horizontal range}} \]