Question

The escape velocity of a projectile on the earth's surface is 11.2 km/s. A body is projected out with thrice this speed. The speed of the body far away from the earth will be?

• A. 22.4 km/s
• B. 31.7 km/s
• C. 33.6 km/s
• D. None of these

Hint:

When an object is projected with speed higher than the escape velocity, its final velocity at infinity will be directly related to the initial speed.

Answer 1

The Correct Option is B

The escape velocity \( v_e \) is the minimum speed needed for an object to escape the gravitational pull of the earth. If a body is projected with thrice this velocity, the speed of the body at infinity will be: \[ v_{\infty} = \sqrt{3} \times v_e \] Given that \( v_e = 11.2 \text{ km/s} \), then: \[ v_{\infty} = \sqrt{3} \times 11.2 = 31.7 \text{ km/s} \] Thus, the speed of the body far away from the earth is 31.7 km/s.