The earth's radius is about 4000 miles. Kampala, the capital of Uganda, and Singapore are both nearly on the equator. The distance between them is 5000 miles. The flight from Kampala to Singapore takes 9.0 hours. What is the plane's angular velocity with respect to the earth's surface? Give your answer in .
The angular velocity of the plane with respect to the earth's surface is .
The angular velocity of the plane is,
Here, is the angular velocity of the time, is the change in angular position of the plane, and is the time period.
The angular position of the plane is,
Here, is the distance between Kampala and Singapore, and is the radius of the earth.
Substitute 5000 miles for and 4000 miles for in the above equation to find .
Substitute for and for in the equation (I) to find .
Therefore, the angular velocity of the plane with respect to the earth's surface is .
You are given the equations that are used to solve a problem. For each of these, you are to
a. Write a realistic problem for which these are the correct equations. Be sure that the answer your problem requests is consistent with the equations given.
b. Finish the solution of the problem, including a pictorial representation.
A rubber ball is dropped onto a ramp that is tilted at 20°, as shown in FIGURE P4.59. A bouncing ball obeys the “law of reflection,” which says that the ball leaves the surface at the same angle it approached the surface. The ball’s next bounce is 3.0 m to the right of its first bounce. What is the ball’s rebound speed on its first bounce?
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