Question

A boat is heading due east at 25 km/hr (relative to the water.) The water current is moving toward the southwest (45° angle) at 10km/hr.

a) Give the vector representing the actual movement of the boat (with respect to the land.)

b) How fast is the boat moving relative to the land?

c) By what angle does the current push the boat off of its due east course?

Answer 1

+x = east, +y = north

velocity of boat relative to water v_b/w = (25 i) km/hr,

velocity of water relative to land v_w/g = 10 [-cos(45) i - sin(45) j] km/hr

a) velocity of boat relative to land v_b/l = v_b/w + v_w/g = (25 i) + 10 [-cos(45) i - sin(45) j] = (17.9 i - 7.1 j) km/hr

b) |v_b/l| = 19.2 km/hr

c) tan^-1(7.1/17.9) = 21.6^o