An airplane flies 850 miles in 1 hour 15 minutes. What is its average speed in miles per hour?

If 820 miles per hour is the ground speed, of course the total path length of the plane in one hour will be 820 miles. But more likely it’s the air speed. So, for example, if the air is moving at 100 miles per hour relative to the ground in the same direction as the plane (jet stream), then the plane will go at 920 miles per hour relative to the ground, and will go 920 miles. In general, if the plane moves at velocity vp relative to the air, and the air moves relative to the ground at velocity va and angle theta from the direction of the plane relative to the air, then the plane will go at velocity sqrt(vp x vp + va x va + 2va x vp cos(theta)) relative to the ground.

On the other hand, suppose you want not the total path length, but the maximum total distance. The Earth is a sphere of radius R approximately 3959 miles. If the plane flies along a great circle to get the maximum straight line distance while keeping at a constant distance R from the center of the Earth, the total straight line distance, will be

2 x R x sin(L/2R) = 818.5 miles,

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