The initial velocity vi required to project a body vertically upward from the surface of the earth to reach a height of 10R, where R is the radius of the earth, may be described in terms of escape velocity ve such that ${v_i} = \sqrt {{x \over y}} \times {v_e}$. The value of x will be ____________.
Answer (integer)
10
Solution
Here R = radius of the earth<br><br>From energy conservation<br><br>${{ - G{m_e}m} \over R} + {1 \over 2}m{v_i}^2 = {{ - G{m_e}m} \over {11R}} + 0$<br><br>${1 \over 2}m{v_i}^2 = {{10} \over {11}}{{G{m_e}m} \over R}$<br><br>${v_i} = \sqrt {{{20} \over {11}}{{G{m_e}} \over R}}$<br><br>${v_i} = \sqrt {{{10} \over {11}}} {v_e}$<br><br>{$\because$ escape velocity ${v_e} = \sqrt {{{2G{m_e}} \over R}}$}<br><br>Then the value of x = 10
About this question
Subject: Physics · Chapter: Gravitation · Topic: Escape Velocity
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