Velocity and acceleration mathematics question!
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Question

amtran_bus · Answer

A lemming marches off an ice berg, falling directly downward from a height of 12.40 ethers. 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?

goformit100 · Answer

Why am i Tagged here ?

amtran_bus · Answer

you gave me a medal.

klimenkov · Answer

I really don't know what to do especially via matrix operations. But I would take an expression $\text{altitude = }at^3+bt^2+ct+d$, put the values for t (0, 0.1, 0.2, 0.3) and put the values for the altitude. And then i'd got a system of the linear equations. And solve it using matrix operations.

amtran_bus · Answer

If you don't mind, could you show me what the equation would be?

Like 12.40T3?

klimenkov · Answer

The first one will be
$12.4=a\cdot0^3+b\cdot0^2+c\cdot0+d$
Because at the moment $t=0$ the lemming was at the height = 12.4 meters.
Then you will have 4 equtions and 4 variables - a,b,c,d. Solve and find the law of the falling.

amtran_bus · Answer

Oh my goodness.  This one is ROUGH!

amtran_bus · Answer

Oh well.

amtran_bus · Answer

But that is for one, correct?

klimenkov · Answer

$\text{altitude = }-4.9t^2-32t+12.4$

amtran_bus · Answer

Wow, thanks, how did you get that?

klimenkov · Answer

Calculate.

klimenkov · Answer

You should do this calculation by yourself. Be honest.

amtran_bus · Answer

Thanks @klimenkov