Question

A rocket in orbit just above the atmosphere is moving in uniform circular motion. The radius of the circle in which it moves is 6.381 × 106 m, and its centripetal acceleration is 9.8 m/s2 . What is the speed of the rocket?

Answer 1

Centripetal acceleration is given by the formula

$a_{cen}= \frac{v^2}{r}$

Since we know the value of the acceleration is 9.8 m/s² and we know r, we can solve for the speed, which is the magnitude of v.  Note the value of a is just the acceleration due to gravity, which is what makes the rocket orbit and not fly off into space.

$9.8 \frac{m}{s^2}=\frac{v^2}{6.381 \times 10^6m} \\ \\ 9.8 \frac{m}{s^2} \times 6.381 \times 10^6m=v^2 \\ \\ v= \sqrt{9.8 \frac{m}{s^2} \times 6.381 \times 10^6m} =24755 \frac{m}{s}$