Question

A stone is projected at an angle of \(30\degree\) to the horizontal. The ratio of kinetic energy at projection to its kinetic energy at the highest point is:

• A. 4 : 3
• B. 4 : 1
• C. 1 : 2
• D. 1 : 4

Hint:

For projectile motion:
• At the highest point, only horizontal velocity contributes to kinetic energy.
• Use trigonometric components to relate initial and final kinetic energies.

Answer 1

The Correct Option is A

1. Kinetic Energy at Projection: \[ KE_{\text{projection}} = \frac{1}{2} m u^2. \]
2. Kinetic Energy at the Highest Point: Horizontal velocity remains constant: \[ KE_{\text{highest}} = \frac{1}{2} m (u \cos 30^\circ)^2. \]
3. Ratio: \[ \frac{KE_{\text{projection}}}{KE_{\text{highest}}} = \frac{u^2}{u^2 \cos^2 30^\circ} = \frac{1}{\cos^2 30^\circ} = \frac{4}{3}. \]

Final Answer: \( \boxed{4 : 3} \)