Question

The earth's radius is about 4000 miles. Kampala, the capital ofUganda, and Singapore are both nearly on the equator. The distancebetween them is 5000 miles.

1.Through what angle do you turn, relative tothe earth, if you fly from Kampala to Singapore? Give your answerin degrees and then in radians

2.The flight from Kampala to Singapore takes 9hours. What is the plane's angular velocity relative to theearth?

Answer 1

1) Angle to be turned = 1.25 radian = 71.62°

2) Angular velocity = 3.85 x 10⁻⁵ rad/s

Step-by-step explanation:

1) Refer the figure.

We need to find the angle.

We have relation

Arc length = Radius x Angle

5000 = 4000 x Angle

Angle = 1.25 radian

`\texttt{Angle = }1.25* (180)/(\pi)=71.62^0`

Angle to be turned = 1.25 radian = 71.62°

2) Angular displacement = Angular velocity x Time

time = 9 hours = 32400 s

1.25 = Angular velocity x 32400

Angular velocity = 3.85 x 10⁻⁵ rad/s