A child is in danger of drowning in the Merimac river. The Merimac river has a current of 3.1 km/hr to the east. The child is 0.6 km from the shore and 2.5 km upstream from the dock. A rescue boat with speed 24.8 km/hr (with respect to the water) sets off from the dock at the optimum angle to reach the child as fast as possible. How far from the dock does the boat reach the child?
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Nice question. First step: draw a diagram of this situation.
2. choose a coordinate system. If I were you, I'd make the dock the origin of a cartesian system where the river is running along the y-axis.
3. Given that, write down an equation for the position of the child at time t.
4. Then write down an equation for the position of the boat.
5. Then find the point where the boat and child meet actually meet.
6. Finally find the distance of this point from the dock.
**correction: the river is running along the x-axis. From negative x (west) to positive x (east)
What if I was to assume that the child was at a fixed location?