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**1. Homework Statement**

A child's pogo stick stores energy in a spring (k=2.5 x 10^4 N/m). At position

**(x_1=-0.1m), the spring compression is a maximum and the child is momentarily at rest. At position**

*A***(x=0), the spring is relaxed and the child is moving upward. At position**

*B***, the child is again momentarily at rest at the top of the jump. There is a displacement (x_2) above the x=0 mark. Assuming that the combined mass of the child and pogo stick is 25kg, a) Calculate the total energy of the system if both potential energies are zero at x=0, b) determine x_2, c) calculate the speed of the child at x=0, d) determine the value of x for which the kinetic energy of the system is a maximum, and e) obtain the child's maximum upward speed.**

*C***2. Homework Equations**

E(before)=E(after)--- Both Potential and Kinetic

**3. The Attempt at a Solution**

I wasn't able to find a) right off the bat. The answer I got (125J) does not match the answer in the back of the book (101J). What I did to find a) was put: U(spring)= KE(after) , and to find U(spring) I used:

1/2kx^2 --> 1/2(2.5 x 10^4 N/m)(-0.1m)^2

That should give you 125J but again, it doesn't match the answer given. Am I doing something wrong? Something about the displacement of the spring?

I got b) right I think. To find x_2 I used KE(before)=U_g(after), so:

1/2mv^2=mgh ---> 101J(Used book's answer)= (25)(9.8)h

I solved for h and i got .41m, which is supposedly correct. =]

I got c) by using U(spring)=KE(after) so: 101J=1/2(25)v^2; v=2.8425

**So overall, I don't know how to find a), d) or e).**

For both d) and e), how do you know where the KE and speed is maximum?

For both d) and e), how do you know where the KE and speed is maximum?