A firefighter, a distance d from a burning building, directs a stream of water from a fire hose at angle $\theta_{i}$ above the horizontal. If the initial speed of the stream is $v_{i},$ at what height h does the water strike the building?

In a local bar, a customer slides an empty beer mug down the counter for a refill. The height of the counter is 1.22 m. The mug slides off the counter and strikes the floor 1.40 m from the base of the counter. (a) With what velocity did the mug leave the counter? (b) What was the direction of the mug's velocity just before it hit the floor?

A firefighter slides down a pole in a fire station with an acceleration of 6.2 m/s$^{2}$. If the firefighter starts at rest and slides for a distance of 3.7 m, what is his final speed?

A firefighter, $60.0 \mathrm{~m}$ away from a burning building, directs a stream of water from a ground-level fire hose at an angle of $37.0^{\circ}$ above the horizontal. If the water leaves the hose at $40.3 \mathrm{~m} / \mathrm{s}$, which floor of the building will the stream of water strike? Each floor is $4.00 \mathrm{~m}$ high.

For the cellar of a new house, a hole is dug in the ground, with vertical sides going down 2.40 m. A concrete foundation wall is built all the way across the 9.60-m width of the excavation. This foundation wall is 0.183 m away from the front of the cellar hole. During a rainstorm, drainage from the street fills up the space in front of the concrete wall, but not the cellar behind the wall. The water does not soak into the clay soil. Find the force the water causes on the foundation wall. For comparison, the weight of the water is given by

$$2.40 \mathrm{m} \times 9.60 \mathrm{m} \times 0.183 \mathrm{m} \times 1000 \mathrm{kg} / \mathrm{m}^{3} \times 9.80 \mathrm{m} / \mathrm{s}^{2}=41.3 \mathrm{kN}$$

A landscape architect is designing triangular flower beds. Determine the number of different triangles that he can form using the given measurements. Then solve the triangles. Round to the nearest tenth. $a = 8 m , b = 9 m , m \angle A = 35 ^ { \circ }$

A cruise ship sails due north at 4.50 m/s while a Coast Guard patrol boat heads $45.0^{\circ}$ north of west at 5.20 m/s. What are the x-component of the velocity of the cruise ship relative to the patrol boat?

The $20-g$ centrifuge at NASA's Ames Research Center in Mountain View, California, is a horizontal, cylindrical tube $58.0 \mathrm{ft}$ long and is represented. Assume an astronaut in training sits in a seat at one end, facing the axis of rotation $29.0 \mathrm{ft}$ away. Determine the rotation rate, in revolutions per second, required to give the astronaut a centripetal acceleration of $20.0 \mathrm{~g}$.

The function f(h) = 2d+4.3 relates the h height of the water in a fountain in feet to the d diameter of the pipe carrying the water. Graph the function on a calculator and use the graph to find the height of the water when the pipe has a diameter of 1.5 inches.

A vertical electric field of magnitude $2.00 \times 10^{4} \mathrm{N} / \mathrm{C}$ exists above the Earth's surface on a day when a thunderstorm is brewing. A car with a rectangular size of 6.00 m by 3.00 m is traveling along a dry gravel roadway sloping downward at $10.0^{\circ}$ Determine the electric flux through the bottom of the car.

A landscape architect is planning an artificial waterfall in a city park. Water flowing at 1.70 m/s will leave the end of a horizontal channel at the top of a vertical wall h = 2.35 m high, and from there it will fall into a pool. (a) Will the space behind the waterfall be wide enough for a pedestrian walkway? (b) To sell her plan to the city council, the architect wants to build a model to standard scale, which is one-twelfth actual size. How fast should the water flow in the channel in the model?

A fire hose ejects a stream of water at an angle of

$$35.0^\circ$$

above the horizontal. The water leaves the nozzle with a speed of 25.0 m/s. Assuming that the water behaves like a projectile, how far from a building should the fire hose be located to hit the highest possible fire?

The fireman holds the hose at an angle $\theta=30^{\circ}$ with horizontal, and the water is discharged from the hose at $A$ with a speed of $v_A=40 \mathrm{ft} / \mathrm{s}$. If the water stream strikes the building at $B$, determine his two possible distances $s$ from the building. $A$ is $4\text{ ft}$ above the ground and $B$ is $8 \text{ ft}$ above the ground.

A stream of water from a fire hose can be modeled by

$$y = - 0.003 x ^ { 2 } + 0.58 x + 3$$

, where x and y are measured in feet. A firefighter is standing 57 feet from a building and is holding the hose 3 feet above the ground. The bottom of a window of the building is 26 feet above the ground. Your friend claims the stream of water will pass through the window. Is your friend correct? Explain.