# Help with vector exam questions (M1)

1. Aug 31, 2007

### 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 modelled 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

2. Aug 31, 2007

### Staff: Mentor

How does distance relate to velocity and time?

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

Last edited: Aug 31, 2007
3. Aug 31, 2007

### CathyLou

Ok, thanks.

Would I use v = s/t?

Cathy

4. Aug 31, 2007

### chaoseverlasting

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

5. Aug 31, 2007

### learningphysics

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

or you can just use sfinal = sinitial + vt

6. Aug 31, 2007

### Staff: Mentor

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.

7. Aug 31, 2007

### CathyLou

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

Cathy

8. Aug 31, 2007

### learningphysics

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...

9. Aug 31, 2007

### CathyLou

Okay - thanks so much for your help!

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

Cathy

10. Aug 31, 2007

### learningphysics

looks good!

11. Aug 31, 2007

### CathyLou

Thank you.

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

12. Aug 31, 2007

### 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.

13. Aug 31, 2007

### CathyLou

Would I use Pythagoras?

Cathy

14. Aug 31, 2007

### learningphysics

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

15. Aug 31, 2007

### CathyLou

I'm really not sure what to do.

Could you please show me the steps?

Thank you.

Cathy

16. Aug 31, 2007

### learningphysics

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...

17. Aug 31, 2007

### CathyLou

Thank you so much for your help!

Cathy