Question

A 74.5-kg person is on a barrel ride at an amusement park. He stands on a platform with his back to the barrel wall. The tangential velocity of the person is 4 m/s and the centripetal acceleration is 5 m/s/s. What is the radius of the barrel in m? Round to 1 decimal place

Answer 1

The radius of the barrel is 3.2 meters, calculated using the formula for centripetal acceleration given the person's tangential velocity of 4 m/s and a centripetal acceleration of 5 m/s^2.

Step-by-step explanation:

To determine the radius of the barrel in an amusement park barrel ride, where a person experiences centripetal acceleration, we can use the formula that relates centripetal acceleration to tangential velocity and radius:

ac = v2 / r

Where ac is the centripetal acceleration, v is the tangential velocity, and r is the radius of the circular path.

Given the person's tangential velocity (v) as 4 m/s and centripetal acceleration (ac) as 5 m/s2, we can rearrange the formula and calculate the radius:

r = v2 / ac

r = (4 m/s)2 / 5 m/s2

r = 16 m2/s2 / 5 m/s2

r = 3.2 m

Therefore, the radius of the barrel is 3.2 meters, rounding to one decimal place.