Two fun-loving otters are sliding toward each other on a muddy (and hence frictionless) horizontal surface. One of them, of mass 7.50 kg, is sliding to the left at 5.00 m/s while the other, of mass 5.75 kg, is slipping to the right at 6.00 m/s. They hold fast to each other after they collide. (a) Find the magnitude and direction of the velocity of these free-spirited otters right after they collide. (b) How much mechanical energy dissipates during this play?

The lead female character in the movie Diamonds Are Forever is standing at the edge of an offshore oil rig. As she fires a gun, she is driven back over the edge and into the sea. Suppose the mass of a bullet is 0.012 kg and its velocity is +685 m/s. Her mass (including the gun) is 50 kg. (a) What recoil velocity does she acquire in response to a single shot from a stationary position, assuming that no external force keeps her in place? (b) Under the same assumption, what would be her recoil velocity if, instead, she shoots a blank cartridge that ejects a mass of 5.0 x 10-4 kg at a velocity of +685 m/s?

A baseball approaches home plate at a speed of 42.0 m/s, moving horizontally just before being hit by a bat. The batter hits a pop-up such that after hitting the bat, the baseball is moving at 50.0 m/s straight up. The ball has a mass of 145 g and is in contact with the bat for 2.30 ms. What is the average vector force the ball exerts on the bat during their interaction? (Let the +x-direction be in the initial direction of motion, and the +y-direction be up.)

A 45.0 kg girl is standing on a 137 kg plank. The plank, originally at rest, is free to slide on a frozen lake, which is a flat, frictionless surface. The girl begins to walk along the plank at a constant velocity of 1.41 m/s relative to the plank. (Let the direction the girl is moving in be positive. Indicate the direction with the sign of your answer.) (a) What is her velocity relative to the surface of ice? m/s(b) What is the velocity of the plank relative to the surface of ice? m/s

A rocket, which is in deep space and initially at rest relative to an inertial reference frame, has a mass of 86.2 × 105 kg, of which 14.7 × 105 kg is fuel. The rocket engine is then fired for 180 s, during which fuel is consumed at the rate of 480 kg/s. The speed of the exhaust products relative to the rocket is 2.98 km/s. (a) What is the rocket's thrust? After the 180 s firing, what are (b) the mass and (c) the speed of the rocket?

A 52.1-kg person, running horizontally with a velocity of +4.62 m/s, jumps onto a 14.7-kg sled that is initially at rest. (a) Ignoring the effects of friction during the collision, find the velocity of the sled and person as they move away. (b) The sled and person coast 30.0 m on level snow before coming to rest. What is the coefficient of kinetic friction between the sled and the snow? (a) Numberi Units

A rocket, which is in deep space and initially at rest relative to an inertial reference frame, has a mass of 75.8 x 105 kg, of which 15.3 × 105 kg is fuel. The rocket engine is then fired for 410 s, during which fuel is consumed at the rate of 390 kg/s. The speed of the exhaust products relative to the rocket is 2.81 km/s. (a) What is the rocket's thrust? After the 410 s firing, what are (b) the mass and (c) the speed of the rocket? (a) Number i Units (b) Number i Units (c) Number i Units

. The fisherman's mass is 79 kg, and the boat's is 126 kg. The fisherman and boat are initially at rest when the fisherman throws a package of mass m = 15 kg horizontally to the right with a speed of vi = 4.9 m/s. What is the velocity of the boat after the package is thrown? Neglect any resistance force from the water. (Give the magnitude in m/s, and select the correct direction from the options given.)  What is the direction of the boat?

A vacationer of mass 75 kg is standing on a stationary raft of mass 55 kg. The vacationer then walks towards one end of the raft at a speed of 2.3 m/s relative to the water. What are the magnitude and direction of the resulting velocity of the raft relative to the water?

Identical twins, each with mass 52.5 kg, are on ice skates and at rest on a frozen lake, which may be taken as frictionless. Twin A is carrying a backpack of mass 12.0 kg. She throws it horizontally at 2.55 m/s to Twin B. Neglecting any gravity effects, what are the subsequent speeds of Twin A and Twin B?