Question

You are traveling on an airplane. The velocity of the plane with respect to the air is 190 m/s due east. The velocity of the air with respect to the ground is 33 m/s at an angle of 30° west of due north.

1.What is the heading of the plane with respect to the ground? (Let 0° represent due north, 90° represents due east).

2.How far east will the plane travel in 1 hour?

Answer #1

velocity of the air with respect to the ground v' = - 33 * cos(30)
i + 33 sin(30) j

velocity of the air with respect to the ground v' = - 28.58 i +
16.5 j

1)

The velocity of the plane with respect to the ground v " = v + v '
= 161.42 i + 16.5 j

tan^-1(16.5/161.32)

**Heading of plane = 5.84 ^{0} north of
East**

2)

Distance = speed * time

Speed in east = 161.42 m/s

Distance = 161.42 * 1 * 60 *60 m

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