Escape Velocity and Projection – Rankers Physics

Gravitational Potential Energy: Practice Problem & Solution

The escape velocity of a body on the earth surface is 11.2 km/s. If the same body is projected upward with velocity 22.4 km/s, the velocity of this body at infinite distance from the centre of the earth will be
11.2 km/s
\(11.2\sqrt{3} \text{km/s}\)
\(11.2\sqrt{2} \text{km/s}\)
Zero

Solution Explained:

To solve this problem, we apply the core principles of Gravitational Potential Energy. Understanding the underlying formula is key to arriving at the correct answer below:

By conservation of energy, \(v_{\infty} = \sqrt{v^2 - v_{\text{esc}}^2} = \sqrt{(2v_{\text{esc}})^2 - v_{\text{esc}}^2} = v_{\text{esc}}\sqrt{3} = 11.2\sqrt{3} \text{km/s}\).

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