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Deadeye Martin fires a 18-g arrow at a speed of 40 m/s at a 150-g apple tossed straight into the air by his friend Jaquette. If the arrow arrow travels straight through the apple at the peak of the apple’s trajectory, and the apple’s speed is 1.8 m/s after the collision, what is the speed of the arrow immediately after hitting the apple?

Hecelina drives her horse to pull her wagon up a long, shallow hill. The horse and wagon together have a mass of 1800 kg, and the horse provides a constant force of 1000 N directing the wagon up the hill. The hill rises a vertical distance of 8.0 m, and the hill is 85 m long along the slope. With what starting speed must Hecelina drive her horses so that they barely make it to the top of the hill before stopping? Neglect any drag forces.

Firefighters connect a fire hose to a hydrant and lift the other end of the hose into the air to attack a fire in an upper floor. In the ground just below the hydrant the gauge water pressure is 138 kPa, the pipe has a diameter of 6.0 cm, and the volume flow rate through the pipe is 0.04 m3/s. If the gauge water pressure is zero at the end of the hose, which has a diameter of 5.0 cm, to what height did the firefighters lift the hose?

In the figure, a cylindrical L-shaped pipe is connected to a cylindrical tank. The absolute pressure at point B is 180 kPa, and the density of the oil is 900 kg/m3. What is the mass of the floating piston? (The figure shows the system which is filled with oil and consists of a hollow closed vertical cylinder and an L-shaped pipe connected to the middle of its lateral surface. The cylinder has a height of 60 centimeters and a base diameter of 20 centimeters. The top base of the cylinder is marked A. The bottom base of the cylinder is marked B. The pipe has a width of 4.0 centimeters. The vertical part of the pipe has the oil column of 100 centimeters with a piston on it.)

In the figure, a cylindrical L-shaped pipe is connected to a cylindrical tank. The absolute pressure at point B is 150 kPa, and the density of the oil is 900 kg/m3. What is the mass of the piston? (The figure shows the system which is filled with oil and consists of a hollow closed vertical cylinder and an L-shaped pipe connected to the middle of its lateral surface. The cylinder has a height of 60 centimeters and a base diameter of 20 centimeters. The top base of the cylinder is marked A. The bottom base of the cylinder is marked B. The pipe has a width of 4.0 centimeters. The vertical part of the pipe has the oil column of 100 centimeters with a piston on it.)

Marie and Maria each send a spinning uniform disc towards the center of an axle. Marie’s disk has a mass of 0.5 kg with a radius of 15 cm and is spinning about the axle at a rate of 100 rpm. Maria’s disk also has a mass of 0.5 kg, but a radius of 20 cm, and it spins in the same direction as Marie’s at a rate of 150 rpm. The two discs then collide and stick together. What is their final rotational speed in rad/s?

A team of six people work to lift a platform of cargo with a mass of 300 kg up a cliff with a single rope and pulley. If the cargo rises with a constant speed of 1.2 m/s, how much power must each person provide?

In a riveting and apparently infuriating game of croquet, Pierre and Regnault launch their identical croquet balls, which have masses of 0.45 kg each, at each other instead of the wickets. Pierre fires his north at a speed of 5 m/s, and Regnault sends his south at a speed of 7 m/s. The balls collide midair, sending Regnault’s ball directly east at a speed of 4 m/s. In what direction does Pierre’s ball go after the collision? 

Hecelina drives her horse to pull her wagon up a long, shallow hill. The horse and wagon system have a mass of 1800 kg, and the horse provides a constant force of 1000 N directing the wagon up the hill. The hill rises a vertical distance of 8.0 m, and the hill is 85 m long along the slope. With what starting speed must Hecelina drive her horses so that they barely make it to the top of the hill before stopping? Neglect any drag forces.

The most typical way to overload a muscle group when participating in a resistance training program is to