Question

In an amusement park ride, a rider suspended by cables swings back and forth from a tower. The maximum speed v (in meters per second) of the rider can be approximated by v=2gh, where h is the height (in meters) at the top of each swing and g is the acceleration due to gravity (g≈9.8 m/sec^2). Determine the height at the top of the swing of a rider whose maximum speed is 15 meters per second. Round your answer to the nearest tenth.

Answer 1

According to the equation for the maximum speed, it is found that the height at the top of the swing of the rider is of 0.8 m.

What is the equation for the maximum speed?

As stated in the problem, it is given by:

v = 2gh.

In which:

• v is the maximum speed.

• g is the gravity.

• h is the height.

In this problem, the parameters are g = 9.8, v = 15. Hence we can solve for h to find the height.

v = 2gh

2 x 9.8h = 15

19.6h = 15

h = 15/19.6

h = 0.8.

The height at the top of the swing of the rider is of 0.8 m.

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