Calculating Change in Distance of Two Cars Traveling in Opposite Directions

[musicmar]

Homework Statement

Car A is traveling west at 60 km/hr.
Car B is traveling 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.

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.

V_A = (-60 km/hr) i

V_B = (-70 km/hr) j


So,

r_A = (-60t + x) i

r_B = (-70t + y) j


z = r_B + r_B = (-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.

 

[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.