Problem involving rates of change of distance.

[CaptainBlood]

Two cars start moving form the same place. One goes north at a rate of 50 mi/hr, while the other heads east at a rate of 30 mi/hr. At what rate is the distance between the two cars changing exactly two hours later?

 

I thought that the equation for the velocity vectors is:

 

r(x) = 30xi + 50yj

 

and thus distance d two hours later is given by:

 

d = √(30x² + 50x² )

 

and

 

dd/dt = ∂x/dt + ∂y/dt

 

and after solving the equation I just plug in 2 for x and y to get what time the distance changes at the two hour mark.

 

Is this right?

[Hal.]

This is how I would approach this problem . I am assuming that this is a flat earth scenario .

 

First , I would find a formula to calculate the position of the car that is travelling east .

 

I would then find a formula to calculate the position of the car that is travelling north .

 

Next , I would find a formula for the distance between these two positions .

 

Also , I would differentiate this formula to give me the rate of change of distance with respect to time .

 

The rate of change I calculated is a constant number of miles per hour .

 

I think that may help .

 

 

Edited July 12, 2011 by Hal.

[CaptainBlood]

OK, thanks, I did it.