A boat moving at 5 mi/hr is ti cross a river in which the current is flowing at 3 mi/hr. In what direction should the boat head in order to reach a point on the other bank of the river directly opposite its starting point?
draw a diagram. The upstream angle is θ such that
sinθ = 3/5
where straight across is θ=0
Well, my dear friend, it seems like this boat is in quite a predicament. If it simply heads straight across the river, the current will push it downstream. On the other hand, if it heads directly against the current, it's going to have to work extra hard to make any progress. So, what's the solution?
I'm going to let you in on a little secret: the boat needs to use its navigation skills and head at an angle. If it steers upstream, at an angle against the current, it will end up being pushed diagonally across the river while still making some forward progress. It's like trying to walk in a straight line while your goofy cousin is pushing you from the side – you have to lean into it!
So, to reach the opposite bank from its starting point, this boat needs to steer slightly upstream, at an angle that compensates for the downstream current. It's all about finding that sweet spot where the boat can cross the river and still maintain its sense of direction, just like finding the perfect balance between knock-knock jokes and epic puns!
To reach a point directly opposite its starting point, the boat needs to head in a direction perpendicular to the river current. In this case, the boat should aim straight towards the opposite bank of the river.
To determine the direction in which the boat should head in order to reach a point directly opposite its starting point, we need to take into account the velocity of the boat and the velocity of the river current.
The boat needs to counteract the effect of the river current to reach the point directly opposite its starting point. Therefore, the boat should head in a direction that compensates for the sideways drift caused by the river current.
Here's how you can calculate the direction:
1. Determine the resultant velocity of the boat.
- The resultant velocity is the vector sum of the velocity of the boat relative to still water and the velocity of the river current.
- Since the boat is moving at 5 mi/hr and the current is flowing at 3 mi/hr, the resultant velocity can be calculated by subtracting their vectors.
- In this case, since the current is flowing in a different direction from the boat's desired destination, we subtract the vectors: 5 mi/hr - 3 mi/hr = 2 mi/hr.
2. Determine the heading direction of the boat.
- The heading direction of the boat should be in the opposite direction of the resultant velocity vector.
- Since the resultant velocity vector is 2 mi/hr, the boat should head directly into the opposite direction of the current.
- Therefore, the boat should head upstream (against the current).
By heading upstream, the boat's forward motion will counteract the sideways drift caused by the river current, allowing it to reach a point directly opposite its starting point.