CHAPTER 10

1. (P.299 Prob.34) A cannon tilted up at a 30° angle fires a cannon ball at 80 m/s from atop a 10-m-high fortress wall. What is the ball's impact speed on the ground below?
2. (P.300 Prob.38) The spring in Figure P10.38a is compressed by length Dx. It launches the block across a frictionless surface with speed v₀. The two springs in FigureP10.38b are identical to the spring of Figure P10.38a. They are compressed by the same length Dx and used to launch the same block. What is the block's speed?
   
3. (P.300 Prob.44) A 1000-kg safe is 2.0 m above a heavy-duty spring when the rope holding the safe breaks. The safe hits the spring and compresses it 50 cm. What is the spring constant of the spring?
4. (P.301 Prob.54) A pendulum is formed from a small ball of mass m on a spring of length L. As Figure P10.54, a peg is height h = L/3 above the pendulum's lowest  point. From what minimum angle θ must the pendulum be released in order for the ball to go over the top of the peg without the string going slack?
   
5. (P.301 Prob.58) a 100-g balll moving to the right at 4.0 m/s collides head-on with a 200-g ball that is moving to the left at 3.0 m/s.
   a. If the collision is perfectly elastic, what are the speed and direction of each ball after the collision?
   b. If the collision is perfectly inelastic, what are the speed and direction of each ball after the collision?
6. (P.303 Prob.72) Challenge Problem. A 2.0-kg cart has a spring with k = 5000 N/m attached to its front, parallel to the ground. This cart rolls at 4.0 m/s toward a stationary 1-kg cart.
   a. What is the maximum compression of the spring during the collision?
   b. What is the speed of each cart after the collision?