Question

A small plane flies at 200 km/h in still air. If the wind blows directly out of the west at 50.0 km/h, (a) in what direction must the pilot head her plane to move directly north relative to the ground and (b) how long does it take her to reach a point 300 km directly north of her starting point?

Answer 1

Answer:

a)θ=74.03°  (N-E)

b)t=1.56 hr

Explanation:

Given that

Plane speed = 200 km/h

Wind speed = 55 km/h

Now from diagram

V is the resultant velocity of plane

$200^2=V^2+55^2$

V=192.28 km/h towards north

From triangle ABC

$cos\theta =\dfrac{55}{200}$

θ=74.03°

Given that

d=300 km

We know that

d = V x t

300 = 192.28 x t

t=1.56 hr