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Suppose that you have a spring gun that you use to launch a small metal ball. You try the first two settings of the gun. The first setting compresses the spring by 1and fires the ball a distance of 0.25 . The second setting compresses the spring by 2 and fires the ball a distance of 1 .Assuming that the relationship between springcompression and height is quadratic, how far will the ball go at the highest setting, which compresses the spring 3
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Answer #1

let compression be denoted by x and distance by s
we know 0.5*k*x2 = m*g*s + c

so k*x2 = 19.6*m*s + 2c

x2 = A*s + B

so for x =1 we have s=0.25

for x=2 we have s = 1

substituting these and solving for A and B

we get

A = 4 and B = 0

so for x = 3 we get 9 = 4*s

so s = 9/4 m = 2.25m

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