Question

suppose that the radius of the circular path is r when the speed of the rocket is v and the acceleration of the rocket has magnitude a. if the radius and speed are increased to 2r and 2v respectively, what is the magnitude of the rocket's subsequent acceleration?

Answer 1

When both the radius and speed of a rocket on a circular path are doubled, the subsequent centripetal acceleration is twice the original acceleration, or 2a.

Step-by-step explanation:

The magnitude of Rocket's Subsequent Acceleration

The question concerns the centripetal acceleration experienced by a rocket moving in a circular path.

Initially, the rocket moves at speed v on a path with radius r and has a centripetal acceleration of magnitude a.

According to the formula for centripetal acceleration, ac = v2/r, if the radius (r) and speed (v) of the rocket are both doubled, the new centripetal acceleration can be calculated by plugging the new values into the formula, ac = (2v)2/(2r).

This simplifies to ac = 4v2/2r, which further simplifies to ac = 2v2/r.

Therefore, the new acceleration is twice the initial acceleration, so the rocket's subsequent acceleration would be 2a.