Question

A body is fired from the surface of the earth. It goes to a maximum height R(radius of the earth) from the surface of the earth. Find the initial velocity given.

• A. 6.9 km s^-1
• B. 7.4 km s^-1
• C. 7.9 km s^-1
• D. 8.4 km s^-1

Answer 1

Answer: (C)

7.9 km s^-1

Answer 2

$\frac{1}{2}mv^{2} = GMm\left\lbrack \frac{1}{R} - \frac{1}{2R} \right\rbrack$

or v = $\sqrt{\frac{GM}{R}}$

= $\sqrt{\frac{6.67 \times 10^{- 11} \times 6 \times 10^{24}}{6400 \times 10^{3}}} = 7.9kms^{- 1}$.