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I've gotten through about 3/4 of a large problem that I'm working through in my book (no solution manual FTL). Here's my question...

## Homework Statement

A pole P of mass 300kg and length L of 12m is approaching Matt(80kg, no motion) at 8.28 m/s on a frictionless surface. Matt has a massless spring loaded launcher loaded with a mass N of .5kg.

Matt plans to save himself by shooting the mass N at the pole P approaching him, propelling himself away from the pole while simultaneously slowing the velocity of the pole when the masses hit the pole. Here I am assuming the mass N hits the pole at the poles center of mass and sticks.

The spring constant of the massless spring launcher is 3x10

^{2}J/m

^{2}

1.) Determine the speed of the pole when it reaches the frictionless surface.

-I've solved this already, it is 8.28m/s

2.)Determine Matt's velocity when he and the pole have the same velocity.

3.) Determine how fast the mass N must be going in order to slow down the pole appropriately.

4.)Determine how much Matt should compress the spring before releasing it.

## Homework Equations

I'm assuming the use of conservation of energy equations will be useful in this problem. However some equations that I'm not seeing as relevant may be missing.

Kinetic energy:

E = mv

^{2}

Spring Potential energy:

E = kx

^{2}

-Where x is (Uncompressed - compressed) length.

## The Attempt at a Solution

All the questions depend on one another, this becomes a problem when I can't solve the second of four questions in sequence.

Question 2: Determine Matt's velocity when he and the pole have the same velocity.

-I'm having trouble with this problem, it seems to me that we would need to know more information about the situation before being able to solve, however, this class is my first exposure to physics, and I am most likely wrong. Any help would be greatly appreciated.

Question 3: Determine how fast the mass N must be going in order to slow down the pole appropriately.

-Since I have no answer for number two, I will be assuming that both Matt and the pole P have the same velocity at 6.28m/s. Please check my logic.

LOGIC:

The velocity of Pole P needs to be changed by 2m/s. (8.28m/s initial velocity - 6.28m/s final velocity = 2m/s)

Initial energy of pole at 8.28m/s: .5 x 300kg x (8.28m/s)^2 = 10290 J

Energy of pole at needed velocity of 6.28m/s : .5 x 300kg x (6.28m/s)^2 = 5766 J

10290J - 5766J = 4524J

So the small mas N (.5kg) that Matt shoots from his launcher at the pole needs to transfer 4524J of energy to slow the pole by 2m/s.

4524J = .5 x .5kg x V

^{2}

V = 134.5 m/s

Question 4: Determine how much Matt should compress the spring before releasing it.

As determined in question three, we know that the mass N that is shot out of the spring launcher needs an energy of 4524J in order to slow the speed of the pole P by 2m/s. Here is where I run into a logical problem.

All of the problems I've solved in HW sets thus far related to spring energy had the spring attached to a static object. However, in this problem on one side of the spring is Matt (80kg), on the other is mass N(.5kg). I'm not sure how to model this using the potential spring energy equation because I know that when the spring is allowed to uncompress, some of the energy will be given to Matt, and some to the mass N. Any help getting me going here will also be greatly appreciated.

I understand the the length of my question is probably less than desirable. However, please know that any help given is greatly appreciated, and will be reciprocated if possible.(I'm more of a math and computer science guy)