Velocity of Motorist with Respect to Police Car at Intersection

[sylenteck0]

Homework Statement

Two highways intersect. A police car P is 800 m west from the intersection and moving at 80km/h west. Motorist M is 600m north of the intersection and moving at 60 km/h south.
a) in the unit-vector notation, what is the velocity of the motorist with respect to the police car?
b) How does the direction of the velocity found in a) compare to the line of sight between the two cars
c) If the cars maintain their velocities, do the answers to A and B change as the cars move nearer to the intersection?

Homework Equations

The Attempt at a Solution

Well, I'm assuming that we're going to use i and j, so I got this:
m= 0i+600mj p=800mi+0 j

Now, I'm unsure where I'm supposed to put the velocity of each car in. Or for that matter, how am I supposed to present the velocity of the motorist in respect to the police car? Am I just supposed to subtract the two vectors?

Thanks :)

 

[rootX]

Am I just supposed to subtract the two vectors?

Thanks :)

Yes.
In other words, try to make the co-ordinates of the police car to 0,0 by subtracting each point by the position vector of police car.

So, that would give you the relative of motor.. relative to the car.
Now differentiate, and get the velocities equations.

I did this question like last week lol

you need to read the section prior to solving these questions, and I am assuming that you haven't. That halliday book provides good enough introduction to relative motions.

btw. this is the question from halliday? That's from where I did this question.

 

[sylenteck0]

Yup. Thanks for the advice :)

 

[sylenteck0]

I've tried subtracting the one vector from another, but I can't find a way to get the derivative; it always ends up as zero because there's no variable. What would serve as the variable in this case?

 

[rootX]

I've tried subtracting the one vector from another, but I can't find a way to get the derivative; it always ends up as zero because there's no variable. What would serve as the variable in this case?

but you are provided both velocities(or dx/dt).
so like dp/dt = something

 

[sylenteck0]

So I could theoretically use the velocities in place of the coordinates themselves?

m= 0i+ 16.66m/s t j
p=22.22m/s t i+ 0 j

Something like that? I can see finding the derivative that way =P