Donald A.

Firemen use a high-pressure hose to shoot a stream of water at a burning building. The water has a speed of 25.0 m/s as it leaves the end of the hose and then exhibits projectile motion. The firemen adjust the angle of elevation $\alpha$ of the hose until the water takes 3.00 s to reach a building 45.0 m away. Ignore air resistance; assume that the end of the hose is at ground level. (a) Find $\alpha$. (b) Find the speed and acceleration of the water at the highest point in its trajectory. (c) How high above the ground does the water strike the building, and how fast is it moving just before it hits the building?

At its Ames Research Center, NASA uses its large "20-G" centrifuge to test the effects of very large accelerations ("hypergravity") on test pilots and astronauts. In this device, an arm 8.84 m long rotates about one end in a horizontal plane, and an astronaut is strapped in at the other end. Suppose that he is aligned along the centrifuge's arm with his head at the outermost end. The maximum sustained acceleration to which humans are subjected in this device is typically 12.5$g$. (a) How fast must the astronaut's head be moving to experience this maximum acceleration? (b) What is the $difference$ between the acceleration of his head and feet if the astronaut is 2.00 m tall? (c) How fast in rpm (rev/min) is the arm turning to produce the maximum sustained acceleration?

Two piers, $A$ and $B$, are located on a river; $B$ is 1500 m downstream from A ($\textbf{Fig. E3.32}$). Two friends must make round trips from pier $A$ to pier $B$ and return. One rows a boat at a constant speed of 4.00 km/h relative to the water; the other walks on the shore at a constant speed of 4.00 km/h. The velocity of the river is 2.80 km/h in the direction from $A$ to $B$. How much time does it take each person to make the round trip?

Two blocks connected by a light horizontal rope sit at rest on a horizontal, frictionless surface. Block $A$ has mass 15.0 kg, and block $B$ has mass $m$. A constant horizontal force $F$ = 60.0 N is applied to block $A$ ($\textbf{Fig. P4.40}$). In the first 5.00 s after the force is applied, block $A$ moves 18.0 m to the right. (a) While the blocks are moving, what is the tension $T$ in the rope that connects the two blocks? (b) What is the mass of block $B$?

In a truck-loading station at a post office, a small 0.200-kg package is released from rest at point A on a track that is onequarter of a circle with radius 1.60 m ($\textbf{Fig. P7.57}$). The size of the package is much less than 1.60 m, so the package can be treated as a particle. It slides down the track and reaches point $B$ with a speed of 4.80 m/s. From point $B$, it slides on a level surface a distance of 3.00 m to point $C$, where it comes to rest. (a) What is the coefficient of kinetic friction on the horizontal surface? (b) How much work is done on the package by friction as it slides down the circular arc from $A$ to $B$?

Block $A$, with weight $3w$, slides down an inclined plane $S$ of slope angle 36.9$^{\circ}$ at a constant speed while plank $B$, with weight $w$, rests on top of A. The plank is attached by a cord to the wall $\textbf{(Fig. P5.97).}$ (a) Draw a diagram of all the forces acting on block $A$. (b) If the coefficient of kinetic friction is the same between $A$ and $B$ and between $S$ and $A$, determine its value.