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 ...


 
Independence of Perpendicular Components of Motion
It is often said that perpendicular components of motion are independent of each other. A horizontal motion is independent of vertical variables of motion and a vertical motion is independent of horizontal variables.

The motion of a boat across a river involves two simultaneous and independent motions - the motion perpendicular to the river banks and the motion parallel to the river banks. The motion perpendicular to the river banks is dependent upon the variables that are directed across the river - river width and boat velocity. The river velocity, being perpendicular to the crossways motion of the boat, does not affect the time to cross the river.


 
If a boat heads straight across a river, then it is the motor of the boat that provides the power to carry the boat perpendicular to the river's banks. While the boat heads towards the opposite shore, it is the current that provides the power to carry the boat parallel to the river's banks. The current simply carries the boat down the river and has no effect upon the motion perpendicular to the banks of the river (see Know the Law section). Thus, the time to cross the river is dependent upon the speed at which the boat heads across the river and the distance it must travel across the river (see Formula Frenzy section). Wider rivers take more time to cross. Slower boat velocities lead to greater times of travel.


 
For a boat that heads straight across a river, the distance which it travels downstream is dependent upon the time of travel and the river velocity in accordance with the formula:
 
ddownstream= vriver• time