Suppose you have a spring-loaded projectile launcher. Aim it straight upwards, c

Question

Suppose you have a spring-loaded projectile launcher. Aim it straight upwards, compress the spring 1 cm, then launch a projectile from rest. that it rises 20 cm above the end of the spring. If you repeat this experiment, but instead compress the spring by 2 cm, should you expect the projectile to rise more than, less than, or exactly 40 cm above the end of the spring? Can you explain this conclusion in terms of energy? I am having trouble. My answer was: The launcher will launch the object more than 40 cm because the height is squared not doubled. but I found out that this was wrong. Any help would be great!

Explanation / Answer

we have,

1/2 kx2 = mgh

ie h = kx2 / 2mg

for x = 1 cm --- h = 20 cm

So, for x = 2cm --- h = 80 cm

Therfore, the answer is greater than 40 cm

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