1- A trampoline artist of mass 66 kg jumps vertically upwards from the top of a

Question

1- A trampoline artist of mass 66 kg jumps vertically upwards from the top of a platform. When he reaches the trampoline, 3 m below, he is travelling with a speed of 9.5 m s-1.
If the trampoline behaves like a spring of spring constant 4.9 x 104 N m-1, how far does he extend it?

( Don't forget the gravitational potential energy that also goes into the extension.)
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2- What should be the spring constant of a spring designed to bring a 1440 kg car to rest from a speed of 82 km h-1 so the occupants undergo a maximum deceleration of 5.7g?
Answer to 2 significant figures.

( Must use energy conservation as force is not constant!)

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3- What should be the spring constant of a spring designed to bring a 1070 kg car to rest from a speed of 100 km h-1 so the occupants undergo a maximum deceleration of 4.9g?
Answer to 2 significant figures.

(Must use energy conservation as force is not constant!)

Explanation / Answer

1- m = 66 kg, h = 3 m, v = 9.5 m/s, k = 4.9 x 104 N/m, find x

mv2/2 + mgx = kx2/2

kx2/2 - mgx - mv2/2 = 0

x = 0.362 m

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