# Calculus

The pilot of an airplane that flies with an airspeed of 800 km/h wishes to travel to a city 800 km due east. There is a 80 km/h wind FROM the northeast

a) what should the plane's heading be?
b) How long will the trip take?

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1. A is angle he heads North of East
plane velocity due to wind in East direction = -80 cos 45
plane velocity due to heading in East dir = 800 cos A
total East component = 800 cos A - 80 cos 45

plane velocity due to wind in North direction = -80 sin 45
plane velocity due to heading in North dir = 800 sin A

We want ZERO North resultant so
800 sin A = 80 sin 45
sin A = 0.1 (.707) = 0.0707
A = 4 degrees North of East or 90 - 4 = 86 deg compass heading

now velocity component East = 800 cos 4 - 80 cos 45
= 798 - 56.56 = 741 km/hr East
800 / 741 = hours taken

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Damon

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