1. The problem statement, all variables and given/known data A child's pogo stick stores energy in a spring (k=2.5 x 10^4 N/m). At position A (x_1=-0.1m), the spring compression is a maximum and the child is momentarily at rest. At position B (x=0), the spring is relaxed and the child is moving upward. At position C, 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. 2. Relevant 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?