1. Some sliding rocks approach the base of a hill with a speed of 11.0 m/s . The hill rises at 43.0 above the horizontal and has coefficients of kinetic and static friction of 0.440 and 0.580, respectively, with these rocks. Start each part of your solution to this problem with a free-body diagram. a) Find the acceleration of the rocks as they slide up the hill. Express your answer in meters per second squared. b) Once a rock reaches its highest point, will it stay there or slide down the hill? stay there or slide down the hill c) If it slides down, find its acceleration on the way down, else enter 0. Express your answer in meters per second squared.

2. A 56.0 kg ice skater spins about a vertical axis through her body with her arms horizontally outstretched, making 1.50 turns each second. The distance from one hand to the other is 1.5 m. Biometric measurements indicate that each hand typically makes up about 1.25 % of body weight. a) What horizontal force must her wrist exert on her hand? Express your answer in newtons. b) Express the force in part (a) as a multiple of the weight of her hand. Express your answer as a multiple of weight.

3. A flat (unbanked) curve on a highway has a radius of 220.0 m. A car rounds the curve at a speed of 28.0 m/s . a) What is the minimum coefficient of static friction that will prevent sliding? b) Suppose that the highway is icy and the coefficient of friction between the tires and pavement is only one-third what you found in the previous part. What should be the maximum speed of the car so it can round the curve safely? Express your answer with the appropriate units.

4. A 51.0 kg stunt pilot who has been diving her airplane vertically pulls out of the dive by changing her course to a circle in a vertical plane. a) If the plane's speed at the lowest point of the circle is 96.0 m/s , what is the minimum radius of the circle so that the acceleration at this point will not exceed 4.00 g ? Express your answer with the appropriate units. b) What is the apparent weight of the pilot at the lowest point of the pullout? Express your answer with the appropriate inits.