A boat leaves one bank of a river and heads straight across, due north, at 4 m/s relative to the…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A boat leaves one bank of a river and heads straight across, due north, at m/s relative to the water. The river is metres wide and flows due east at m/s. Write the velocity of the boat over the ground as a vector, taking east as the direction and north as the direction. Find the speed over the ground, the angle between the path and north, the time to cross and how far downstream the boat lands.
Need a reminder? The key ideaShow
Vectors add by components, and scales every component. Forces in balance add to the zero vector. The vector from to is .
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The sum. metres per second.
Step 2. The speed. metres per second.
Step 3. The angle. Measured from north, , so .
Step 4. The time. The boat crosses metres northwards at metres per second, so the time is seconds.
Step 5. The drift. The current carries the boat metres east.
Answer: m/s, east of north, seconds and metres downstream.
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