Question

How fast would you have to drive around a circle of radius 30 feet (10 m) to experience an acceleration equal to the acceleration due to gravity?

a) 10 ft/s
b) 20 ft/s
c) 30 ft/s
d) 40 ft/s

Answer 1

To experience an acceleration equal to gravity while driving around a circle with a 30-foot radius, you would need to travel at approximately 30 ft/s, which is option c).

Step-by-step explanation:

To determine how fast you would have to drive around a circle of radius 30 feet to experience an acceleration equal to the acceleration due to gravity, we can use the formula for centripetal acceleration, which is a = v^2/r. Here, a represents the centripetal acceleration, v is the linear velocity, and r is the radius of the circular path. The acceleration due to gravity (g) is approximately 9.8 m/s2 or about 32.2 ft/s2. To find v, we can rearrange the formula to v = √(a × r) and substitute a with g. Thus, we calculate v as √(32.2 ft/s2 × 30 ft).

When you calculate this, you get v ≈ 31 ft/s. Among the options provided, the closest answer is c) 30 ft/s. Therefore, you would have to drive at approximately 30 ft/s to achieve a centripetal acceleration equal to the acceleration due to gravity.