Calculating Displacement & Airspeed with Wind Speed

[barthayn]

wind speed?

Homework Statement

A car leaves point A and drives at 80.0km/h [E] for 1.50h. It then heads north at 60.0 km/h for 1.00 h and finally [30^o W of N] at 100.0 km/h for 0.50 h, arriving at point B.
a) Determine the displacement of point B from point A.
b) A plane flies directly from point A to point B, leaving 2.00h after the car has departed from point A. It arrives at point point at the B at the same time the car arrives. There is a wind blowing at 60.0 km/h due south for the entire trip. What is the airplane's airspeed?
c) What direction must the plane head in order to arrive at point B?
d) How long would the plane's trip be if there was no wind?

Homework Equations

Other then SOH CAH TOA, I have no idea

The Attempt at a Solution

Used vectors to solve for part a. No idea for the other parts because my teacher hasn't taught the class with wind speed, and this is due for Tuesday

 

[Gib Z]

How long is the plane flying for? You drew a vector diagram for the first part, so in which direction is the plane flying and how far did it fly? From this you can work out b).

After you have worked that out, you have found the resultant velocity of the plane. This is infact the sum of the winds velocity and the planes velocity in the direction it is actually heading in (against the wind) . This is similar to having to swim against the current to get across a river - if you just tried to swim straight, you would drift down the river. So draw up a triangle that relates the 3 vectors and use the sine and cosine rules to analyse the triangle, which will give you c).

The analysis from c) should tell you the speed the plane is actually capable of, without the wind, which should yield d).