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# Physics: time to reach shore, velocity of ice skaters, shuff

In the following problems, the answers are given. Show the working to arrive at the answers.

1. To get off a frozen, frictionless lake, a 65 kg person takes a 0.150 kg shoe and throws it horizontally, directly away from the shore with a speed of 2 m/s. If the person is 5 m from the shore, how long does he take to reach it?
Answer: - 1.08 x10^3 s = 18.1 min

2. Two ice skaters not paying attention collide in a completely inelastic collision. Prior to the collision, skater 1 with a mass of 60 kg, has a velocity of 5 km/h eastward, and moves at a right angle to skater 2, who has mass of 75 kg and a velocity of 7.5 km/h southward. What is the velocity of the skaters after the collision?
Answer: - 4.7 km/h at an angle of 62* south of east.

3. A moving shuffleboard puck has a glancing collision with a stationary puck of the same mass. If the friction is negligible, what are the speeds of pucks after collision? ...Vin = 0.95m/s
Answer: - V1 = 0.61 m/s and V2 = 0.73 m/s

4. In a high speed chase, a policeman's car bumps a criminal's car directly from behind to get his attention. The policeman's car is moving at 40 m/s to the right and has a total mass of 1800 kg. The criminal's car is initially moving in the same direction at 38 m/s. His car has a total mass of 1500 kg. Assuming an elastic collision, determine their two velocities immediately after the bump.
Answer: - Vp = 38.2 m/s, Vc = 40.2 m/s, both in same direction as initially moving.

5. Two cups are placed on the uniform board that is balanced on a cylinder. The board has a mass of 2 kg and is 2 m long. The mass of the cup 1 is 200 g and it is placed 1.05 m to the left of the balance point. The mass of the cup 2 is 400g. Where should the cup 2 be placed for balance (relative to the right end of the board)?