A radar station sends a signal to a ship which is located a distance 14.0 kilometers from the station at bearing 136° clockwise from the north. At the same moment, a helicopter is at a horizontal range of 19.6 kilometers, at bearing 152° clockwise from the north, with an elevation of 2.58 kilometers. Let east be the î direction, north be the ĵ direction, and up be the  direction.   (A) What is the displacement vector (in km) from the helicopter to the ship? (Express your answer in vector form. Do not include units in your answer.)   (B) What is the distance (in km) between the helicopter and ship?   (C)  The ship begins to sink at a rate of 5.40 m/s. Write the position vector (in km) of the ship relative to the helicopter as a function of time as the ship sinks. Assume that the helicopter remains hovering at its initial position and that the sinking rate remains the same even after the ship sinks under the surface. (Use the following as necessary: t. Do not include units in your answer.)

Vector C has a magnitude of 22.2 m and points in the −y‑ direction. Vectors A and B both have positive y‑ components, and make angles of α=42.4 and β=26.7 with the positive and negative x- axis, respectively. If the vector sum A+B+C=0 , what are the magnitudes of A and B?

A sailboat race course consists of four legs, defined by the displacement vectors ABC, and, as the drawing indicates. The magnitudes of the first three vectors are A = 2.70 km, B-5.30 km, and C= 4.40 km. The finish line of the course coincides with the starting line. Using the data in the drawing, find (a) the distance of the fourth leg and (b) the angle. 23.0 (a) Number (b) Number Units Units B Finish- K 35.0 X 40.0⁰ Start

A jogger travels a route that has two parts. The first is a displacement A of 2.65 km due south, and the second involves a displacement → B that points due east. The resultant displacement A + B has a magnitude of 4.75 km. (a) What is the magnitude of B, and (b) what is the direction of A + B as a positive angle relative to due south? Suppose that A - B had a magnitude of 4.75 km. (c) What then would be the magnitude of B, and (d) what is the direction of A - B relative to due south? (a) Number i (b) Number i (c) Number i (d) Number i Units Units Units Units > > >