Applied Maths help?

koolkakool

Hi. im in 5th year at the moment, and im doing applied maths as an extra subject.Im stuck on a problem in relative velocity:

Two straight roads cross at right angles at 0. M and N jog towards 0 at 4m/s and 1 2/3m/s respectively. Calculate the magnitude and direction of the velocity M with respect to N. When M was at 0, N was 50m beyond 0. Calculate the shortest distance they were apart.

I got 4 1/3 m/s and East 22' 37' South for velocity, but i dont know how to figure out the shortest distance between them, anyone here know how to do it?. Thanks

EDIT: Its on the bottom of page 104 in Fundamental Applied Mathematics by Oliver Murphy

Fringe

I hate relative velocity but to get the shortest distance, find the perpendicular distance with one of the velocities relative to the other. You've got the relative velocities. Draw a diagram. The perpendicular distance is the shortest distance. You can either find this distance using trigonometry or coordinate geometry using the perp dist formula.

I'm not too good at relative velocity but this site has a pretty good explanation
http://www.skoool.ie/skoool/examcentre_sc.asp?id=2589

MathsManiac

Just to clarify Fringe's suggestion: you need to draw a diagram showing things relative to N. That is, pretend N is fixed at the origin. Plot M's position relative to N at the known instant. Then daw a line representing M's motion relative to N, using what you've already worked out. The perp. distance from the origin to that line is the shortest distance between them.

koolkakool

thanks a lot both of you , i finally got it. it was really beginning to annoy me.