Question

If I swing a bucket of water in a circle above my head, on a string of 1.5 m, and it takes 0.5 seconds to make one revolution, then what is the velocity of the bucket?

a. 2.1 m/s
b. 18.8 m/s
c. 9.4 m/s
d. 3.0 m/s

Answer 1

The velocity of the bucket swung in a circle can be calculated by dividing the circumference of the circle by the time per revolution. Using the given radius of 1.5 meters and time of 0.5 seconds, the velocity is found to be 18.84 m/s, which is approximately 18.8 m/s.

Step-by-step explanation:

To find the velocity of the bucket, we can use the formula for the circumference of a circle (C = 2πr) and divide that by the time it takes to complete one revolution. The radius (r) is the length of the string, which is given as 1.5 m. The time (T) for one revolution is 0.5 seconds.

First, calculate the circumference of the circle the bucket is making:

• C = 2πr = 2 π × 1.5 m = 3π m ≈ 9.42 m

Now, divide the circumference by the time to get the velocity (v):

• v = C/T = 9.42 m/0.5 s = 18.84 m/s

Therefore, the correct answer is b. 18.8 m/s.