# Homework Help: Relative motion

1. Oct 18, 2009

### musicmar

1. The problem statement, all variables and given/known data

Car A is travelling west at 60 km/hr.
Car B is travelling north at 70 km/hr.
The cars intersect at point O.
When Car A is x km east of and Car B is y km south of O, the distance between the cars is z km.
Find the rate of change of z when x = .8 km and y = .6 km.

3. The attempt at a solution

In my physics class, we would do this problem with anti-derivatives with initial conditions.
However, in my calc class, we haven't learned this yet.

VA = (-60 km/hr) i

VB = (-70 km/hr) j

So,

rA = (-60t + x) i

rB = (-70t + y) j

z = rB + rB = (-60t + x) i + (-70t + y) j

From here, do I take the derivative of z to get dz/dt?

Also, if someone could tell me how to start this problem without using anti-derivatives, that would be great.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Oct 18, 2009

### LCKurtz

You are given dx/dt, dy/dt and know z2 = x2 + y2, where all the variables are functions of t.

Differentiate this equation implicitly with respect to t and plug your numbers in.