Question

Calculate the speed with which a body has to be projected vertically from the Earth’s surface, so that it escapes the Earth’s gravitational influence. (R = 6.4 × 103 km; g = 9.8 m/s²)

Answer 1

R = 6.4×10³ km = 6.4×10⁶ m
g = 9.8 m/s²

Escape velocity, $V_e = \sqrt{ \frac{2GM}{R} }$

$V_e = \sqrt{ \frac{2GM}{R} } =\sqrt{2 \times \frac{GM}{R^2} \times R } =\sqrt{2 \times g \times R } \\ \\ \Rightarrow V_e= \sqrt{2 \times 9.8 \times 6.4 \times 10^6} =11.2 \times 10^3\ m/s\\ \\ \Rightarrow V_e=11.2\ km/s$

So the body should be projected at 11.2 km/s