Question

A boy pushes his sister on a circular swing. What is the speed of his sister on the swing if the boy counts 90 complete swings in 300 seconds and the radius is 1.2 meters?

Answer 1

To find the speed of the sister on the swing, first determine the frequency of the swings and then calculate the circumference of the path. Multiplying these two values gives a speed of 2.26 meters per second.

Step-by-step explanation:

To calculate the speed of the sister on the swing, we first need to determine the frequency of the swings, which can be found by dividing the number of complete swings by the total time taken. The frequency (f) is then 90 swings / 300 seconds = 0.3 swings per second. Each complete swing corresponds to a circular path with a circumference, which can be calculated using the formula C = 2πr. The radius (r) is given as 1.2 meters.

The circumference of the circular path of the swing is thus 2π(1.2 m) = 7.54 meters (rounded to two decimal places). To find the linear speed (v) of the sister on the swing, we then multiply the circumference by the frequency: v = C × f, which results in 7.54 m * 0.3 s-1 = 2.26 meters per second as the speed of the sister on the swing.