# Need some help on vector question

1. Oct 6, 2004

### krypt0nite

An airplane is heading due north at a speed of 300km/h. If a wind begins blowing from the southwest at a speed of 50km/h(average), calculate (a) the velocity (magnitude and direction) of the plane, and (b) how far off course it will be in 30 min.

Ok, I solved a) 337km/h 6 degrees E of N.
But I dont' understand how to solve part b.
Anyone want to help?

2. Oct 6, 2004

### chroot

Staff Emeritus
The plane intended to be moving due north at 300 km/hr, so it should be 150 km due north after 30 minutes.

The wind blew it off-course, however, and it actually moved 337/2 km, six degrees east of north.

Draw a triangle, one leg pointing due north with length 150, another leg pointing six degrees east of north with length 337/2 (168.5), then solve for the length of the third leg. The length of the third leg is the distance between the plane's intended and actual positions after 30 minutes.

- Warren

3. Oct 6, 2004

### krypt0nite

i got 24.8km but the answer sheet says 17.6km.

4. Oct 6, 2004

### Diane_

It depends on what you mean by "how far off course". If you think about it, at the end of half an hour the plane will be 25 kilometers due northeast of where it should be. This is the result of the 300 kph of the plane's still-air speed plus the 50 kph due northeast from the wind. Clearly, the only thing moving the plane off course is the wind.

If you decompose the vectors, you have an isosceles right triangle with hypotenuse 25 km, making the legs 17.6 km. So, one could argue that it's only 17.6 km east of where it should be, and 17.6 km north of where it should be.

5. Oct 6, 2004

### krypt0nite

Okay, guys I need help on another question.

An automobile travelling 90km/h, overtakes a 1.0km train travelling the same direction on a track parallel to the road. If the train's speed is 60km/h, how long does it take the car to pass it and how far will it have travelled in this time? What are the results if the car and train are travelling in opposite directions?

Same Direction: t=.033hours d=3 km
Opposite Direction t=.0067 hour d=.6 km

I don't understand why my distances are wrong. My times are correct though.
The answers are d=2km for same direction and d=.4km for opposite direction.

Can anyone explain this to me?

6. Oct 6, 2004

### Atheist

Displaying how you derived your results would be much more helpfull than telling "I got x=y" because it would save us the time to guess what you did.

However: In this case I think you calculated out how far the car travelled while the question was supposed to be how far the train travels (doesn´t seem obvious to me what´s asked for - as in your 1st question). Hence the factor 60/90 = 2/3 difference between your results and the book´s.

btw.: Your book (or teacher - whoever gave you the questions) suxx.