Question

The spacecraft designers have decided that the 150 m radius spacecraft only needs to produce an acceleration of 12 m/s2 . what speed will produce that acceleration?

a. 8 m/s
b. 16 m/s
c. 24 m/s
d. 36 m/s

Answer 1

The speed that produces a centripetal acceleration of 12 m/s² in a 150 m radius circular path is calculated to be 42.43 m/s based on the formula a = v² / r. However, this speed is not listed in the provided options, suggesting there may be an error in the question.

To determine the speed that will produce an acceleration of 12 m/s² for a spacecraft with a 150 m radius, we can use the formula for centripetal acceleration: a = v² / r, where a is the acceleration, v is the velocity, and r is the radius of the circular path.

By rearranging the formula to solve for v, we have:

v = √(ar) = √(12 m/s² * 150 m) = √(1800) m²/s² = 42.43 m/s.

However, since this speed is not one of the options provided, and we are expecting one of the given speeds (a-c) to be the answer, it's possible there may have been a typo or misunderstanding in the question itself. Therefore, we cannot confidently select an answer from the provided options.