Physics of River Crossing: Solving for Angle and Component Velocity

[asheik234]

Homework Statement

A boat can travel a speed vB in still water. The boat needs to cross a river of width D from point A to point B on the opposite side directly across. On this particular day, the river's current has a speed of vR. Answer the following in terms of D, vB, and vR. For parts (a) and (b), the boat attempts crossing by pointing itself perpendicular to the river's current as shown.

(a) What is the angle θ?(b) What is the component of the boat's velocity that is parallel to the dotted path?

 

[cybhunter]

if your familiar with the real and imaginary plane system, it may look a little bit easier to handle.

There are two vectors, VB and VR (Vectors always contain a magnitude and a direction). The interaction of this two vectors will create a new vector dependent upon the angle difference and the magnitude. The key here is knowing what vector must VB be to cancel out the effects of VR

Hope this helps
Joe

 

[cheahchungyin]

Assume that the boat does not resist any movement of current and follows the flow while still traveling towards the other side at its whole speed simultaneously.

angle= tan^-1(Vr/Vb) <---this is the direction of the resultant velocity.Component of boat's velocity will still be Vb.