# phys

An airplane is heading due south at a speed of 590 km/h. If a wind begins blowing from the southwest at a speed of 65.0 km/h (average).

Calculate magnitude of the plane's velocity, relative to the ground.

Calculate direction of the plane's velocity, relative to the ground.

Calculate how far from its intended position it will be after 15.0min if the pilot takes no corrective action.

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1. wind blows plane Northeast
V = + 65 cos 45 i -590 j + 65 sin 45 j
= +46 i - 590 j + 46 j
= 46 i - 544 j

|V| = sqrt (46^2+544^2) = 546

tan theta = 544/46
theta = 85 degrees south of East
= 85+90 = 175 clockwise from North or about South by 1/2 point East

In 1/4 hour should have gone 147.5 South
in fact went
(1/4)546 sin 85 South = 136 South
and (1/4)546 cos 85 East = 11.9 East

error vector = 11.9 i + (147.5-136) j
= 11.9 i + 11.5 j

error = sqrt(11.9^2 + 11.5^2)
=16.5 km

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2. I typed in the answer for the direction (85 and 175) and they are both wrong according to the problem. I want to try 4.8 degrees since it says east of south, but I don't know though.

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3. What the last comment said is wrong although the reasoning that the southwest wind will get a 45 degree angle is true, the next step is addition between the vector of the wind and the vector of the airplane. Then pitagoras you get the magnitude

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