Relative Acceleration: Calculating Heather's Acceleration Relative to Jill

[student 1]

Homework Statement

Heather in her Corvette accelerates at the rate of 3i -2j (m/s^2) while Jill accelerates at 1i+3j (m/s^2). They both start from rest at the origin of an xy coordinate system. After 5 seconds A. what is Heather's speed with respect to Jill. B. How far apart are they? C. what is Heather's acceleration relative to Jill?

Homework Equations

unit Vector subtraction

The Attempt at a Solution

I know the acceleration is simply subtracting Jill from heather. I believe the speed is multiplying both of them by 5 then subtracting jill from heather. How do you determine the distance? Or would the distance be how I am doing speed?

 

[dirk_mec1]

Remember your kinematics:

$$s = s_0 + v_0 \cdot t + \frac{1}{2}at^2$$
$$v =a \cdot t + v_0$$

and so on...

Now determine what you know and which formula to use.

 

[student 1]

Would you subtract the two vectors for the distance or would you add them? I'm just making sure that you add them, because in the other two parts you subtract.

 

[tiny-tim]

Hi student 1!

Would you subtract the two vectors for the distance or would you add them? I'm just making sure that you add them, because in the other two parts you subtract.

Not following you … what other two parts?

Jill is an inertial observer (as is Heather, of course), so you can use the Newtonian principle of Relativity and "go with Jill", and still get the right results.

So once you've found the relative acceleration, apply that to everything, just as if Jill were stationary.

 

[student 1]

Like the Acceleration of Heather with respect to Jill looks like
Ah+Ahj= Aj so Ahj=Aj-Ah. with vectors.

 

[alphysicist]

Hi student_1,

Like the Acceleration of Heather with respect to Jill looks like
Ah+Ahj= Aj so Ahj=Aj-Ah. with vectors.

I don't think your equation here is quite right--there seem to be some sign errors.

But about whether to add or subtract to find the distance, try picking some easy cases you can see right away. What if the positions of the objects are at x=3 and x=7? or perhaps at x=-4 and x=4?

(Of course, this is just to determine if it's an addition or subtraction. Since your vectors are a two-dimensional case you have some more steps to do to find the distance.)

 

[MrUeda]

I know this is from last year, but I figured that I would add a response that I think would make more sense.

If Jill's acceleration is represented by the vector 1 i + 3 j, then her velocity would be represented by the vector 1t i + 3t j by take the integral of the acceleration vector. Then, plugging in t = 5s, Vj = 5 i + 15 j.

Likewise, Heather's velocity would wind up being 15 i - 10 j.

Then, the relative velocity would be Vh - Vj = 10 i -25 j or 26.9 m/s.

The rest of the problem can be done the same way.