Question

A boat travelling at 30km/h relative to water is headed away from the bank of a river and downstream. The river is 1/2 km wide and flows at 6km/h. The boat arrives at the opposite bank in 1.25min.

Calculate the component of the boat's velocity directed across the river.
Calculate the total downstream component of the boat's motion.

What does it mean headed downstream? Is it going to be the resultant vector?

Answer 1

I guess we should work in seconds and meters
vb = v boat = 30,000/3600 = 8.33 m/s
c = current = 6,000/3600 = .167 m/s

w = width = 500 m

time to cross = 75 s

so say the boat heads at an angle T to the direction of the opposite shore toward the ocean downstream.
Then the only component across the river is vb cos T = 500/75 = 6.67 m/s
so
500 = 75 * 8.33 cos T
cos T = .800
T = 37 deg
now the component of the boat speed downriver measured on the boat is 8.33 sin T = 5 m/s but we also are drifting with the current downstream at .167 m/s
so total component downstream = 5.167 m/s