Answer :
To find the plane's angular velocity relative to the earth's surface, we need to first determine the plane's linear velocity. We know that the distance between Kampala and Singapore is 5000 miles and the flight takes 7.7 hours, so the plane's average speed is 5000/7.7 = 649.4 miles per hour.
Next, we need to convert the linear velocity to angular velocity by dividing it by the earth's radius. Angular velocity is measured in radians per hour, so we need to convert the units of linear velocity from miles per hour to miles per hour per hour (miles/hour²).
The earth's radius is about 4000 miles, so the plane's angular velocity is:
649.4 miles/hour / 4000 miles = 0.16235 radians/hour
To convert this to degrees per hour, we need to multiply by 180/π:
0.16235 radians/hour * 180/π = 9.303 degrees/hour
Therefore, the plane's angular velocity relative to the earth's surface is 9.303 degrees/hour.
To find the plane's angular velocity relative to the Earth's surface, follow these steps:
1. Determine the angular distance traveled: Divide the linear distance between Kampala and Singapore (5000 miles) by the Earth's radius (4000 miles).
Angular distance = 5000 miles / 4000 miles = 1.25 radians
2. Convert radians to degrees: Multiply the angular distance in radians by the conversion factor (180°/π).
1.25 radians * (180°/π) ≈ 71.6°
3. Calculate the angular velocity: Divide the angular distance in degrees by the flight time (7.7 hours).
Angular velocity = 71.6° / 7.7 hours ≈ 9.3°/hr
The plane's angular velocity relative to the Earth's surface is approximately 9.3 degrees per hour.
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