1. The problem statement, all variables and given/known data There are two problems, but I think that they are similar: A toy gun shoots a projectile straight up. The maximum height reached by the projectile is H when the spring is compressed x cm. For the projectile to reach a height of 2H, the spring of the gun should be compressed how much? The bumper of a car is connected to the body by a spring of spring constant k. When the car hits a cement wall with a speed of 1.0 km/h, the spring compresses 1.0 cm. If the car hits a cement wall with a speed of 2.0 km/h, the spring will compress by how much? (answer in cm) 2. Relevant equations The work of the spring is Ws = -.5*k*x^2 The force of the spring is F=-kx 3. The attempt at a solution Problem 1: If work is force * distance, then the equation of the work of the spring can be set equal to the equation for the force of the spring * the distance H: -k*x*H = -.5*k*x^2 after some algebra, you get to this equation: H=1/2x So if you wanted to double H, you would also double x. So in terms of x, the spring should be compressed 2x cm. However, this is not the correct answer, but I think my reasoning is correct. Can somebody point out the flaw? Problem2: If -.5*k*x^2 = .5*m*v^2, you would plug in "2*v" for v because 2km/hr is double 1km/hr Thus, x would be 2 times the original x for 1km/hr, so the spring would compress 2cm. I'm not sure if this problem is correct, because the previous problem is incorrect so I'm not sure about spring problems.