# Matrix operations in a general physics problem

1. Feb 10, 2013

### AmTran_Bus

1. The problem statement, all variables and given/known data

A lemming marches off an ice berg, falling directly downward from a height of 12.40 meters. 0.10 seconds later, he is 9.151 meters above the ocean below. 0.20 seconds this altitude is reduced to 5.804 meters, and at 0.30 seconds he as fallen to 2.359 meters above the ocean.

1. Via Matrix operations, develop a mathematical expression that represents this fall.
2. If the lemming failed to bring an umbrella, how many seconds into this fall would he impact the ocean?
3. If he did have an umbrella to break his fall, and he opened it 7.000 meters above the water, how much time would he have fallen freely prior to opening the umbrella?
4. What would his speed be the instant he opened his umbrella?
5. What is his acceleration due to gravity?

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I know the Times (t) and the altitudes (a)
I know there is an I, J, and K component when dealing with velocity and such in physics.

2. Relevant equations

-Sarrs Law could be used to solve a 3x3 or 2x2 matrix, however, I don't think that is possible for this particular problem.

To find the acceleration, I know to take the f''(x) is required.

3. The attempt at a solution

0, 0.10, 0.20. 0.30 (T)
12.40, 9.151, 5.804, 2.359 (A)

If I new this was right and how to solve this thing, I think I could take the determinant to get part B?

For part C, I think I could plug in the 7.000 into my velocity equation.

Again, without the matrix, I can not derive the first equation.
This is a high school physics problem.

2. Feb 10, 2013

### Simon Bridge

You mean you take $\ddot{f}(t)$ ? Acceleration requires the second time-derivative of displacement.

What is the matrix for the second derivative operation?

However - you want to be able to predict the future positions and speeds.
The trick with this would be setting up the correct vectors.

Well - the lemming is going just downwards so you can get rid of two of the components.

There is no part B or C in your problem as you've written it.

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