Question

Mario programs his helicopter to fly at a target with a velocity (speed and direction) of p. The direction of p is

due east, and its speed is 6 m/s.
To Mario's dismay, the wind causes his helicopter to actually fly with a velocity a, and it misses its target. The
direction of ā is 30° south of east, and its speed is 5 m/s.
(Assume "due east" is 0°, "due north" is 90°, and so on.)
What is the speed of the wind?
m/s
(Round your final answer to the nearest tenth.)
In what direction is the wind blowing?
(Round your final answer to the nearest degree. Your answer should be between 0 and 360°.)

Answer 1

• 3.0 m/s
• 236.3°

Explanation:

The wind speed can be found using the Law of Cosines. It will be the unknown side of a triangle with sides 6 and 5 and included angle 30°.

s^2 = 6^2 +5^2 -2·6·5·cos(30°) ≈ 9.038476

s ≈ √9.038476 ≈ 3.0064 . . . . m/s

The direction of the wind can be found from the Law of Sines, which tells us the relationship of the internal angle A to velocity vector a is ...

sin(A)/a = sin(30°)/3.0064

A = arcsin(5/3.0064·sin(30°) ≈ 56.26°

To find the desired angle, we must add 180° to this value.

The wind is blowing 3.0 m/s in direction 236.3°.