Answer to Question #167359 in Physics for Madison

Question

Carry out the following within the vector PheT simulation.

You are flying a hang glider at 14 mph in the northeast direction (45°). The wind is blowing at 4 mph from due north.

a) What is your airspeed?

b) What angle (direction) are you flying?

c) The wind increases to 14 mph from the north. Now what is your airspeed and what direction are you flying? If your destination is to the northeast, how would you change your speed or direction so you might make it there? Test your answer using the PheT sim.

Answer 1

a)

$$\vec{v}=(14\cos{45},14\sin{45})-(0,4)=(9.9,5.9)\ mph\\v=\sqrt{9.9^2+5.9^2}=11.5\ mph$$

b)

$$\theta=\arctan{\frac{5.9}{9.9}}=30.8\degree\text{ N of E}$$

c)

$$\vec{v'}=(14\cos{45},14\sin{45})-(0,14)\\=(9.9,-4.1)\ mph\\v'=\sqrt{9.9^2+4.1^2}=10.7\ mph$$

$$\theta=\arctan{\frac{4.1}{9.9}}=22.5\degree\text{ S of E}$$