Calculating Man's Northward Distance Traveled with Vector Components

[ch2kb0x]

Homework Statement

Man runs with velocity = 5m/s @ 25 degrees north of east for 10 minutes.
How far to the north of his starting position does he end up?

Homework Equations

The Attempt at a Solution

I know this has got to be the easiest problem to solve but I am not getting it. this is what I did.

It asked for how far to the north, so I assumed they were looking for a final position. I used vector components (5cos25)i + 5(sin25)j, but I don't know how to solve for the distance x. I know there's a formula v = x / t but that didnt help.

 

[phyzmatix]

Vector components is the way to go. They only ask for the distance traveled North, so use the component of the velocity along the y-axis (North) and from that magnitude (speed), you can use your Speed = distance/time equation.

i.e. x = vt

(remember to convert time to seconds).

OR

You could work out his displacement, using Velocity = displacement/time, i.e. Displacement = velocity x time and then break the displacement vector down into components.

Both should give you the same answer.