Vectors and Projectiles - Mission VP6 Detailed Help

A boat begins at point A and heads straight across a 60-meter wide river with a speed of 4 m/s (relative to the water). The river water flows north at a speed of 3 m/s (relative to the shore). The boat reaches the opposite shore at point C. Which of the following would ...


 
An understanding of the motion of a boat across a river demands that one understands two perpendicular and simultaneous motions - the motion of the boat directed perpendicular to the river's banks and the motion of the water directed parallel to the river's banks. These two motions occur simultaneously and independent of each other. The only variable that they share in common is the time of travel.

For a boat heading straight across the river, it is the motor of the boat that provides the powerto carry the boat perpendicular to the river's banks. While the boat heads towards the opposite shore, it is the current that provides the powerto carry the boat parallel to the river's banks. The current carries the boat down the river. And the distance that the boat is carried down the river is dependent upon the time of travel and the speed of the current (see Formula Frenzy section). An increase in either variable - time or river speed - will cause the boat to land downstream a greater distance.

The time of travel is also dependent upon the width of the river and the speed of the boat (see Formula Frenzy section). Wider rivers and lower boat speeds lead to longer crossing times. As such, these two variables indirectly affect the distance traveled downstream by affecting the time of travel.


 
For a boat which heads straight across a river, the distance (dacross) which it travels across (river width) is mathematically related to the time (t) to cross the river and the boat velocity (vboat) in accordance with the formula:
 
dacross= vboat• t
 

The distance which it travels downstream (ddownstream) is dependent upon the time to cross the river (t) and the river velocity (vriver) in accordance with the formula:
 
ddownstream= vriver• t