Velocity of Motorist with Respect to Police Car at Intersection

AI Thread Summary
The discussion focuses on calculating the velocity of a motorist with respect to a police car at an intersection. The motorist's and police car's positions and velocities are established using unit-vector notation. Participants suggest using vector subtraction to find the relative velocity and emphasize the importance of differentiating position vectors to obtain velocity equations. There is confusion about how to incorporate the velocities into the calculations, with advice given to utilize the provided velocities directly. The conversation highlights the need for a solid understanding of relative motion concepts to solve the problem effectively.
sylenteck0
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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 :)
 
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sylenteck0 said:
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 :smile:

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.
 
Yup. Thanks for the advice :)
 
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?
 
sylenteck0 said:
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
 
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
 
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