Answer to Question #148978 in Physics for Michael Duric

Question

A bush pilot wants to fly her plane to a lake that is 250.0 km [N 30.0° E] from her starting point. The plane has an air
speed of 210.0 km/h, and the wind is blowing east at 40.0 km/h.
a) In what direction should she head the plane to fly directly to the lake?
b) Determine her velocity relative to the ground.
c) How long will it take her to reach her destination?
(Note: You must use the sine law and cosine law to answer this question)
SHOW ALL WORK

Answer 1

a)

$$\frac{\sin{30}}{210}=\frac{\sin{a}}{40}\\a=\arcsin{\frac{40\sin{30}}{210}}=5.465\degree$$

$$b=180-(180-30-5.5)=35.5\degree\text{ N of E}$$

b)

$$\frac{\sin{30}}{210}=\frac{\sin{(180-35.5)}}{v}\\v=244\frac{km}{h}$$

c)

$$t=\frac{s}{v}=\frac{250}{244}=1.025\ h$$