(a) Three carts of masses 4.00 kg, 10.0 kg, and 3.00 kg move on a frictionless horizontal track with speeds of 5.00 m/s, 3.00 m/s, and 4.00 m/s, as shown in Figure P9.27. Velcro couplers make the carts stick together after colliding. Find the final velocity of the train of three carts. (b) What If? Does your answer require that all the carts collide and stick together at the same time? What if they collide in a different order?

A 69.0-kg boy and his 37.0-kg sister, both wearing roller blades, face each other at rest. The girl pushes the boy hard, sending him backward with a velocity 3.30 m/s toward the west. Ignore friction. (a) Describe the subsequent motion of the girl. She will move west, in the same direction as her brother, with a speed 3.30 m/s. She will move east, directly away from her brother with a speed 7.8 m/s. She will move east, directly away from her brother with a speed 6.15 m/s. She will move east, directly away from her brother with a speed 1.65 m/s. (b) How much potential energy in the girl's body is converted into mechanical energy of the boy-girl system? J (c) Is the momentum of the boy-girl system conserved in the pushing-apart process? Yes or No

A 0.020 kg bullet is shot horizontally and collides with a 2.00 kg block of wood. The bullet embeds in the block and the block slides along a horizontal surface for 1.50 m. If the coefficient of kinetic friction between the block and the surface is 0.400, what was the original speed of the bullet? Include a diagram of the situation.

The magnitude of the net force exerted in the x direction on a 2.50−kg particle varies in time as show in Figure P9.19. Find the impulse of the force over the 5.00−s time interval,