A boat travelling at 30km/hr 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/hr. The boat arrives at the opposite bank in 1.24 min.

Question

I calculated the perpendicular component of the boat relative to the water as 24km/hr.
I calculated the total downstream component of the boats motion as 24 km/hr (with the parallel component of the velocity of the boat relative to the water at 18km/hr).
And I calculated the direction in which the boat moves relative to land which is 45degrees to the bank.

I need help with calculating the distance the boat moves downstream as it crosses the river.

drwls · Answer

I get (0.5/1.24)*60 = 24.2 km/hr for the perpendicular component. Don't do any rounding off yet.
Parallel component of velocity, relative to water = sqrt[(30^2 - (24.2)^2] = 17.7 km/h

The parallel (downstream) velocity of the boat relative to land is 17.7 + 6 = 23.7 km/hr

The distance it drifts downstream in 1.24 minutes *(23.7 km/h)*(1h/60 min)
= 0.49 km

This agrees well with your 45 degree boat direction relative to land . The downstream drift nearly equals the river's width

Anonymous · Answer

thank you for the help!