Question

You are a member of a geological team in Central Africa. Your team comes upon a wide river that is flowing east. You must determine the width of the river and the current speed (the speed of the water relative to the earth). You have a small boat with an outboard motor. By measuring the time it takes to cross a pond where the water isnt flowing, you have calibrated the throttle settings to the speed of the boat in still water. You set the throttle so that the speed of the boat relative to the river is a constant 6.00 m/s. Traveling due north across the river, you reach the opposite bank in 20.1 s. For the return trip, you change the throttle setting so that the speed of the boat relative to the water is 7.20 m/s. You travel due south from one bank to the other and cross the river in 11.2 s.

b.

What is the current speed?

Answer 1

let velocity of river be V_2 & width be d. velocity of boat relative to river = V_r_1 = 6 m/s going towards north time taken to cross river going north = t_N = 20.1 S Boat velocity relative to still water = V_2 = 7.2 m/s going south time taken to cross the river going south = t_s = 11.2 S \r\n Case I: V_1 rightarrow velocity of boat relative to still water velocity diagram By comparing velocities Implies V_1 = V_r_1 cos theta & V_2 = V_r_1 sin theta width of river = d = v_1 times t_N Implies d = v_1 times 20.1 rightarrow (1) Case II width of river = d = v_2 times t_5 Implies d = 7.2 times 11.2 Implies d = 80.64 m \r\n put value of 'd' in eq^n (1) Implies 80.64 = v_1 times 20.1 Implies v_1 = 4.0119 m/s but v_1 = v_r_1 cos theta Implies 4.0119 = 6 times cos theta Implies cos theta = 0.668 Implies theta = cos^-1 (.668) = 48.0365 degree