A couple Mechanics questions

[kdog3682]

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1) 2 Children of Mass A are on a trampoline. Child 1 is jumping up and down. Child 2 is stationary. Child 2 begins a jump right as Child 1 is on jump #x. They both land at the same time and Child 2 is propelled much higher into the air. Why does this happen?

2) Mass of 5kg and a mass of 10kg, respectively A and B, are placed on a spring. The spring is compressed with 10N of force. Which mass rises higher?

Edit: These are from EK Lecture-Exams

 

[cheesier]

1) View the trampoline as an ideal spring in simple harmonic motion. Remember 1/2mv^2 + 1/2kx^2 = 1/2kA^2 = E1. E2 is 1/2mv^2 + 1/2kx^2 + mg (of Child 1 landing) = 1/2kA^2. You can visualize that if you push a spring that is oscillating down, you are going to give it a greater amplitude. What exactly was the question in the exam?

2) This is a conservation of energy problem . We can assume they're talking about an identical spring in both cases, meaning k is constant. Draw a free body diagram and you'll find that, if we say k = 1, the spring is compressed 110 m for the 10 kg block and 60 m for the 5 kg block. Use conservation of energy and you'll find that the velocity of the 10 k block is a little bit greater than the velocity of the 5 k block at the moment that it is no longer in contact with the spring. Because of this, the 10 kg block goes higher. I could be wrong though.

Edit: Fixed #1