Boat A is located 4km north and 2.5km east of ship B. Ship A with a speed of 22 km/hour is moving south, and ship B with a speed of 40 km/hour is moving at an angle of 37 degrees to the northeast (37 degrees measured from east to north). (a) What is the speed of ship A relative to ship B in unit vector notation (i ̂ for east), (b) when is the separation between the ships the smallest and what is the smallest distance?

Suppose you walk 14.5 m in a direction exactly 19° south of west then you walk 22 m in a direction exactly 39° west of north. Repeat the problem by finding your distance from the starting point in m, but reverse the order of the two legs of the walk. That is, you first walk leg B, which is 22 m in a direction exactly 39 degrees west of north, and then leg A, which is 14.5 in a direction 19 degrees south of west. Please explain how you got your answer in detail.

A plane travels 4 km east and finds itself 5 km North and East of its starting point. Find the y component of the plane's motion and the angle the plane's displacement makes with the x-axis.  (Please explain in steps. I know the answer, but I need help understanding how to get there. Thank you.)

A plane is initially traveling at a speed of 219 km/hr in the direction 38.4° north of west. Three hours later, the plane is traveling at a speed of 204 km/hr in the direction 22.5° west of south. Let +x point due east and +y point due north. (a) What is the x-component of the plane's final velocity (in m/s)? (b) What is the y-component of the plane's final velocity (in m/s)?

Note: Please provide a simple and step-by-step solution.

Problem 2: The figure depicts the sum of two velocities, VA and vg. The magnitude of the sum is 5.5 m/s and the angles shown in the image are 0 = 33", and 0₂-18.3. YA Part (a) Find the magnitude of velocity VA in meters per second. Numeric: A numeric value is expected and not an expression. IVAI=. Part (b) Find the magnitude of velocity vB in meters per second. Numeric A numeric value is expected and not an expression. |VB| = 8₁ 02 VA Va

6. For vectors B = -î – 4ĵ and Å = -31 – 2j, calculate: a. Ā +B and its magnitude and direction angle b. A-B and its magnitude and direction angle.

A plane flies 479 km east from city A to city B in 45.0 min and then 950 km south from city B to city C in 1.10 h. For the total trip, what are the (a) magnitude and (b) direction of the plane's displacement, the (c) magnitude and (d) direction of its average velocity, and (e) its average speed? Give your angles as positive or negative values of magnitude less than 180 degrees, measured from the +x direction (east).

Consider the four displacement vectors A = (3'i+3'j) m, B= (i-4'j) m, C=(-2i+5j) m and an unknown vector D. What is the unknown vector D that will give a resultant displacement 7m directed along negative y axis.

W S →E VIE 0 VbE A boat is crossing the river. By making angle theta = 25 degree with North direction as shown in the figure, the boat can travel due north. If the speed of the boat with respect to the river is 3 m/s. Determine the speed of the river (in m/s) with respect to the earth. Answer to 2 decimal places