An airplane pilot wishes to fly to his destination 500 mi due west, but the wind is blowing at 28.7 mi/hr toward 25.7° north of west. The speed of the plane relative to the air is 169.1 mi/hr. At what angle (south of west) must the pilot orient the plane in order to fly to his destination directly?  If the pilot orients the plane at that angle, what will be the speed of the plane relative to the ground?

Two ships A and B leave the same port at 3:00 p.m. Ship takes a course N 43°43'W at 30 km per hour while B sails due north. At 5:00 pm., B is directly east of A. What is the speed of ship B and what is the distance between the two ships?

To get out of the harbor, a container ship sails at a bearing of 240° for 6 km before changing direction due north. If the container ship travels 15 km north from where it changed direction, what is the bearing of the ship relative to the starting point in the harbor?

An engineer designs a roller coaster so that a car travels horizontally for 152 ft, then climbs 127 ft at an angle of 31.0° above the horizontal. It then moves 127 ft at an angle of 42.0° below the horizontal. If we take the initial horizontal motion of the car to be along the +x-axis, what is the car's displacement? (Give the magnitude of your answer, in ft, to at least four significant figures and give the direction of your answer in degrees counterclockwise from the +x-axis.) magnitude direction 167.6 The magnitude of the displacement is the length of the vector which goes from the starting point to the ending point. You will need to measure this distance, and multiply by your scale factor. ft 367 Measure the angle from the +x-axis to the resultant vector (drawn from the starting point to the ending point). Remember that angles measured counterclockwise from the +x-axis are negative. counterclockwise from the +x- axis Need Help? Read It

In the figure, a radar station detects an airplane approaching directly from the east. At first observation, the airplane is at distance d₁ = 330 m from the station and at angle 0₁ = 41° above the horizon. The airplane is tracked through an angular change A0 = 118° in the vertical east-west plane; its distance is then d₂ = 850 m. Find the (a) magnitude and (b) direction of the airplane's displacement during this period. Give the direction as an angle relative to due west, with a positive angle being above the horizon and a negative angle being below the horizon. de 731 W Airplane d₁ Radar dish

A migrating salmon heads in the direction N 45° E swimming 8. 5 mi/hr relative to the water. The ocean currents in the area flow due East at 3 mi/hr. Find the true velocity of the fish as a vector and find its speed, the magnitude of this velocity vector.

An object moves in a circular path at a constant speed. What is the relationship between the directions of the object's velocity and acceleration vectors?  The velocity vector points in a direction tangent to the circular path. The acceleration is zero. The velocity and acceleration vectors are perpendicular. The velocity and acceleration vectors point in opposite directions. The velocity and acceleration vectors point in the same direction. The velocity vector points toward the center of the circular path. The acceleration is zero.

In an attempt to escape his island, Gilligan builds a raft and sets to sea. The wind shifts a great deal during the day, and he is blown along the following straight lines: 2.50 km 45.0° north of west; then 4.20 km 60.0° south of east; then 1.50 km 25.0° south of west; then 5.30 km straight east; then 1.90 km 5.00° east of north; then 7.20 km 55.0° south of west; and finally 2.90 km 10.0° north of east. What is his final position relative to the island? (i.e., find the magnitude and direction of the displacement.) km at degrees South of East

After flying for 20 min in a wind blowing 39 km/h at an angle of 22° south of east, an airplane pilot is over a town that is 60 km due north of the starting point. What is the speed of the airplane relative to the air?

Dr. B takes her dog ada on a walk. they start out heading south for 0.75 miles. then they turn left 30 degrees and they continue to walk for another 11 mile. Finally they turn right 9o degrees and they walk 1.9 miles. The whole walk takes 45 minutes.  What is the average speed of Dr.B and Ada on their walk? give your answer in m/s. What is the direction of the total displacement vector?