Please show all work 4. 75 trampoline gymnast jumps vertically upward from the t

Question

Please show all work
4. 75 trampoline gymnast jumps vertically upward from the top of a platform with a speed of 4.0m/s. The platform is 3 m above the trampoline. a. If the trampoline behaves like a spring of spring constant5000 N/m, how far does he depress it? Ignore the change in the gravitational energy due to stretching the trampoline. 3.0 m b. Find how far the gymnast depresses the trampoline, taking into account the change in gravitational energy due to stretching the trampoline. Hint: you have to solve a quadratic equation.

Explanation / Answer

a. from energy conservation,

mgh + mv^2 /2 = kx^2 /2

75 x 9.8 x 3 + 75 x 4^2 /2 = 5000x^2 /2

x =1.06 m

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