Question

Problem 11.120 Shore-based radar indicates that a ferry leaves its slip with a velocity v 18 km/h 70°, while instruments aboard the ferry indicate a speed of 18.4 km/h and a heading of 30° west of south relative to the river. Determine the velocity of the river.

Answer 1

Answer:

v_r = 3.1974 km/h @ a = 77.8 degrees south of east

Explanation:

Given:

- velocity of ferry v_f = 18 km / h

- velocity of ferry relative to river v_f/r = 18.4 km /h

Find:

Determine the velocity of the river v_r.

Solution:

- make a graphical representation of the information given as shown:

- Use the vector equations that relates frames:

                                    v_f = v_r + v_f/r

- Use cosine rule on the given representation:

                    v_r^2 = v_f ^2 + v_f/r^2 - 2*v_f/r*v_f*cos(10)

                    v_r^2 = 18^2 + 18.4^2 - 2*18*18.4*cos(10)

                    v_r^2 = 336.3916

                    v_r = 3.1974 km/h

- Use sine law for direction:

                    18 / sin(a)  = 3.1974 / sin 10

                    sin (a) = 0.9775652712

                    a = 77.8 degrees