A yacht is motoring through the Atlantic Ocean just off the coast of North Carolina. The yacht is pointed due east (0.00°). The propellers give the yacht a velocity of 10.2 m/s with respect to the water. The wind is blowing the yacht at a speed of 1.6 m/s at an angle of 75.0°. At the same time, the Gulf Stream is causing the boat to drift at a speed of 3.6 m/s at an angle of 127.5°. What is the resultant velocity of the boat?
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- A ship sets sail from Rotterdam, heading due north at 7.00 m/s relative to the water. The local ocean current is 1.50 m/s in a direction 40.0° north of east. What is the velocity of the ship relative to Earth?Water from a fire hose is directed toward a building as shown in the figure below. The water leaves the hose at a speed of v; = 40.0 m/s and at an angle of 0; = 43.0° above the horizontal. The base of the hose (at ground level) is a horizontal distance d = 49.0 m away from the building. Find the height h (in m) where the water strikes the building. mAt a local swimming pool, the diving board is elevated h = 9.5 m above the pool's surface and overhangs the pool edge by L = 2 m. A diver runs horizontally along the diving board with a speed of vo = 4.9 m/s and then falls into the pool. Neglect air resistance. Use a coordinate system with the horizontal x-axis pointing in the direction of the diver's initial motion, and the vertical y-axis pointing up. Enter an expression for the time ty it takes the diver to fall off the end of the diving board to the pool's surface in terms of vo, h, L, and g. Calculate this time, ty in seconds.Determine the horizontal distance, dy in meters, from the edge of the pool to where the diver enters the water.
- Water leaves a fireman’s hose (held near the ground) with an initial velocity v0 = 23 m/s at an angle θ = 33° above horizontal. Assume the water acts as a projectile that moves without air resistance. Use a Cartesian coordinate system with the origin at the hose nozzle position, as shown. At what horizontal distance d from the building base, where should the fireman place the hose for the water to reach its maximum height as it strikes the building? Express this distance, d, in terms of v0, θ, and g.A pilot starting from Athens, New York, wishes to fly to Sparta, New York, which is 381 km from Athens in the direction 22° N of E. The pilot heads directly for Sparta and flies at an airspeed of 151 km/h. After flying for 2.52 h, the pilot expects to be at Sparta, but instead he finds himself 16 km due west of Sparta. He has forgotten to correct for the wind. (a) What is the velocity of the plane relative to the air? (b) Find the velocity (magnitude and direction) of the plane relative to the ground. (c) Find the wind speed and direction. Please be thorough.A hot air balloon is drifting east at 53 km h-1 . Due to a cross wind, its resultant velocity is 42 km h-1 in a 25° direction. What is the speed and direction of the cross wind?
- A jetliner can fly 6.8 hours on a full load of fuel. Without any wind it flies at a speed of 3.24 x 10² m/s. The plane is to make a round-trip by heading due west for a certain distance, turning around, and then heading due east for the return trip. During the entire flight, however, the plane encounters a 75.9-m/s wind from the jet stream, which blows from west to east. What is the maximum distance (in kilometers) that the plane can travel due west and just be able to return home? Number Units ◄►are 1.0 m and 1.3 m in length. Calculate the tension in each rope. 27 A ship is sailing at 20 km/h N30°E when it encounters a current of 6 km/h from the south. A passenger is walking across the deck with a speed of 5 km/h at an angle of 40° to the starboard (right) of the bow (front) of the ship. What is the velocity of the passenger relative to the ocean floor? canal barge is being pulled along aA marksman fires a practice round from A toward a target B. If the target diameter is 160 mm and the target center is at the same altitude as the end of the rifle barrel, determine the range of "shallow" launch angles for which the round will strike the target. Neglect aerodynamic drag and assume that the round is directed along the vertical centerline of the target. (Note: The word "shallow" indicates a low-flying trajectory for the round.) A Answers: i 885 m/s 0 1420 m ºses i B
- A landscape architect is planning an artificial waterfall in a city park. Water flowing at 0.536 m/s will leave the end of a horizontal channel at the top of a vertical wall h = 2.40 m high and falls into a pool (see figure). (a) How far from the wall will the water land? m Will the space behind the waterfall be wide enough for a pedestrian walkway? (Assume the water must land 2 m from the wall to provide adequate space for a person to walk beneath the waterfall.) Yes No (b) To sell her plan to the city council, the architect wants to build a model to standard scale, one-fifteenth actual size. How fast should the water flow in the channel in the model? m/sA diver springs upward from a board that is 46.0m above the water. At the instant she contacts the water her speed is 12.5m/s and her body makes an angle of 80.4 degrees with respect to the horizontal surface of the water. Determine her initial velocity, both magnitude and direction.The standard height of a basketball hoop is 3.05 m and the standarddistance between the hoop and the free throw line is 4.57 m. If a 1.90 m tall Stephen Curry shoots the ball from the free throw line at an angle of 54.0 degrees with respect to the horizontal, at what speed should the ball leave his hands?