Vectors and Projectiles - Mission VP6 Detailed Help

A boat begins at point A and heads straight across a 80.0-foot wide river with a speed of 8.0 ft/s (relative to the water). The river water flows north at a speed of 6.0 ft/s (relative to the shore). The boat reaches the opposite shore at point C.


 
For a boat that 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


 
A riverboat heading straight across a river involves two simultaneous motions. There is the motion of the boat relative to the water that is directed perpendicular to the banks and powered by the motor of the boat. And there is the motion of the water relative to the shore that is directed parallel to the river's banks and powered by the presence of the current. These two motions occur for the same amount of time. That is, while the boat is moving across the river, the water is flowing down the river. To determine the distance traveled down the river, one must know the time. The only means of determining this time is to use the width of the river and the boat velocity. (See Formula Frenzy section).


 
The key to solving a difficult physics problem is the adoption of an effective strategy. The following strategy will work well.
 
  • Analyze the boat's motion relative to the water to determine the time for the boat to cross the water. The first equation in the Formula Frenzy section above will allow you to determine this time.
  • Analyze the boat's motion relative to the shore to determine the distance traveled down the river. The second equation in the Formula Frenzy section will allow you to determine this distance.