Description : Let's get IceCream!! You have
a boat that has a fixed speed relative to the water, and you want to
get across the river. The simulation initially shows the boat aiming
straight across the river (and ending up downstream). There is a dock
(in grey) directly across the river .. it would be nice to get there.
But there is an IceCream place just upriver from the dock, it would be
BETTER to get there! See how many questions you can answer below before
changing the angle (hint - measure distance across, and distance downriver, and time -
that should allow you to calculate all velocities!).
Enough of this .. let's get IceCream! Find the angle that will let the boat move directly toward the IceCream shack. (The spatial angle to the icecream shack is 36.6 degrees - is that the best angle? Why not?) What angle is needed to exactly arrive at the icecream place? What is the quickest you can cross the stream? How much extra time to go exactly to the dock, to the icecream place?
Note: The calculation to pre-calculate the correct ice cream angle is challenging (beyond our standard effort) .. can you do it? (Hint, think of what physical direction we want to move the boat .. then play with the laws of sines and cosines.) It is easier to use trial and error to get the right angle and then verify the angle with the correct equations than solve the equations for the angle that the boat's vector makes.