Help with vector exam questions (M1)

[CathyLou]

Hi.

I have no idea how to even begin to do this question and so I would really appreciate any help.

Two helicopters P and Q are moving in the same horizontal plane. They are modeled as particles moving in straight lines with constant speeds. At noon P is at the point with position vector (20i + 35j) km with respect to a fixed origin O. At time t hours after noon the position vector of P is p km. When t = 0.5 the position vector of P is (50i - 25j) km. Find

(a) the velocity of P in the form (ai + bj) km/h,

I got this as (60i - 120j) km/h.

(b) an expression for p in terms of t.

Thank you.

Cathy

 

[Doc Al]

How does distance relate to velocity and time?

(This seems better suited for Intro Physics than Calc & Beyond--I'll move it.)

 

[CathyLou]

Ok, thanks.

Would I use v = s/t?

Cathy

 

[chaoseverlasting]

You should start with the basic equations of kinematics and go on from there.

 

[learningphysics]

Ok, thanks.

Would I use v = s/t?

Cathy

Yes, but here s = final position - initial position...

or you can just use sfinal = sinitial + vt

 

[Doc Al]

Would I use v = s/t?

Yes.

You have the initial position vector. You know how each component changes with time, so you can find the position vector at any time t.

 

[CathyLou]

Thanks everyone for your help.

Sorry, but I still don't see how I can get an expression for p in terms of t.

Cathy

 

[learningphysics]

Thanks everyone for your help.

Sorry, but I still don't see how I can get an expression for p in terms of t.

Cathy

p is just the final position in the equation (the final position of helicopter P after t amount of time passes):

v = (final position - initial position)/t

solve for final position... then you can plug in initial position and velocity since you know those already...

 

[CathyLou]

Okay - thanks so much for your help!

I got p = (60t + 20)i + (35 - 120t)j km.

Cathy

 

[learningphysics]

Okay - thanks so much for your help!

I got p = (60t + 20)i + (35 - 120t)j km.

Cathy

looks good!

 

[CathyLou]

Thank you.

I'm not sure now how to do this next part. Could you please help again?

At noon Q is at O and at time t hours after noon the position vector of Q is q km. The velcoity of Q has magnitude 120 km/h in the direction 4i - 3j. Find

an expression for q in terms of t.

Thanks so much!

Cathy

 

[learningphysics]

Try to get the velocity of Q as a vector... Use the magnitude of the velocity which is given... along with a unit vector in the given direction...

So the first step is to get the unit vector in the given direction.

 

[CathyLou]

Try to get the velocity of Q as a vector... Use the magnitude of the velocity which is given... along with a unit vector in the given direction...

So the first step is to get the unit vector in the given direction.

Would I use Pythagoras?

Cathy

 

[learningphysics]

Would I use Pythagoras?

Cathy

Yes... have you studied unit vectors in your class? You divide the vector by its magnitude...

 

[CathyLou]

I'm really not sure what to do.

Could you please show me the steps?

Thank you.

Cathy

 

[learningphysics]

I'm really not sure what to do.

Could you please show me the steps?

Thank you.

Cathy

First step is to find the unit vector in the direction of 4i-3j... so first find the magnitude of this... it is \sqrt{4^2 + (-3)^2} = 5

So then the unit vector in the direction of 4i - 3j is \frac{1}{5}(4i-3j) = \frac{4}{5}i - \frac{3}{5}j

Multiply this vector by 120km/h... and that's your velocity vector. So the velocity of Q is:

120(\frac{4}{5}i - \frac{3}{5}j) = (96i -72j) km/h

Now you can use this velocity to find q... using the fact that the initial position = 0i + 0j... so now it is just like the previous problem...

In general when you need a vector of a particular magnitude in a particular direction... you multiply the magnitude by a unit vector in that particular direction...

Hope this helps...

 

[CathyLou]

Thank you so much for your help!

Cathy