A boat is to be driven from a point on the South bank of a river which flows West-to-East to a destination on the North Bank. The destination is in a direction of N60E from the starting point. The river is 0.2 km wide. The driver of the boat finds that in order to make the trip in a time of 6 min, the boat must maintain a speed of 2.5km/hr relative to water.

Question

A boat is to be driven from a point on the South bank of a river which flows West-to-East to a destination on the North Bank. The destination is in a direction of N60E from the starting point. The river is 0.2 km wide. The driver of the boat finds that in order to make the trip in a time of 6 min, the boat must maintain a speed of 2.5km/hr relative to water. 
a) Find the component of the boat's velocity perpendicular to the bank.
b) Find the downstream component of the velocity contributed by the boat's engines.
c) Find the total downstream component of the boat's velocity.

drwls · Answer

a) (velocity component across)=
(river width)/crossing time)= 2.0 km/hr

b) If the boat's speed with respect to water is 2.5 km/h and the component across the river is 2.0 km/h, the downstream component must be 1.5 km/h (Consider the Pythagorean theorem).

c) Since it travels at a 60 degree angle to the perpendicular to the shore, the total velocity realtive to land is 2.0/cos 60 = 4.0 km/h and the total downstream velocity is 4.0 sin 60 = 3.464 km/h
1.964 km/h of that is the flow velcoity of the river

Shauniechulo · Answer

So this is someone from Pryce's class haha. who asked this?