A 50 kg person, running horizontally with a velocity of 3.0 m/s, jumps onto a 10 kg sled that is initially at rest. Which is the velocity after the collision if the person stick to the sled?

A billiard player sends the cue ball toward a group of three balls that are initially at rest and in contact with one another. After the cue ball strikes the group, the four balls scatter, each traveling in a different direction with different speeds as shown in Figure P10.30. If each ball has the same mass, 0.16 kg, determine the total momentum of the system consisting of the four balls immediately after the collision. FIGURE P10.30

Sand from a stationary hopper falls onto a moving conveyor belt at the rate of 5.00 kg/s as shown in Figure P8.64. The conveyor belt is supported by frictionless rollers and moves at a constant speed of v = 0.750 m/s under the action of a constant horizontal external force Fext supplied by the motor that drives the belt. Find (a) the sands rate of change of momentum in the horizontal direction, (b) the force of friction exerted by the belt on the sand, (c) the external force Fext, (d) the work done by Fext in 1 s, and (e) the kinetic energy acquired by the falling sand each second due to the change in its horizontal motion. (f) Why are the answers to parts (d) and (e) different? Figure P8.64

What exhaust speed is required to accelerate a rocket in deep space from 800 m/s to 1000 m/s in 5.0 s if the total rocket mass is 1200 kg and the rocket only has 50 kg of fuel left?

An estimated force-time curve for a baseball struck by a bat is shown in Figure P9.13. From this curve, determine (a) the magnitude of the impulse delivered to the ball and (b) the average force exerted on the ball. Figure P9.13

A soccer player runs up behind a 0.450-kg soccer ball traveling at 3.20 m/s and kicks it in the same direction as it is moving, increasing its speed to 12.8 m/s. (a) What is the change in the magnitude of the balls momentum? (b) What magnitude impulse did the soccer player deliver to the ball? (c) What magnitude impulse would be required to kick the ball in the opposite direction at 12.8 m/s, instead? (See Section 6.1.)

A 100-g firecracker is launched vertically into the air and explodes into two pieces at the peak of its trajectory. If a 72-g piece is projected horizontally to the left at 20 m/s, what is the speed and direction of the other piece?

Starting with equations m1v1=m1v1cos1+m2v2cos2 and 0=m1v1cos1+m2v2sin2 for conservation of momentum in the x- and y -directions and assuming that one object is originally stationary, prove that for an elastic collision of two objects of equal masses, 12mv12=12mv22+mv1v2cos(12) as discussed in the text.

A car crashes into a large tree that does not move. The car goes from 30 m/s to 0 in 1.3 m. (a) What impulse is applied to the driver by the seatbelt, assuming he follows the same motion as the car? (b) What is the average force applied to the driver by the seatbelt?

The magnitude of the net force exerted in the x direction on a 2.50-kg particle varies in time as shown in Figure P9.10 (page 244). Find (a) the impulse of the force over the 5.00-s time interval, (b) the final velocity the particle attains if it is originally at rest, (c) its final velocity if its original velocity is 2.00im/s, and (d) the average force exerted on the particle for the time interval between 0 and 5.00 s. Figure P9.10