. A boat moving at a speed of 9.8 km/h relative to the water in a river wants to get to a fishing camp that is 5.2 km upstream. If the speed of the water in the river is 6.0 km/h, how long will it take the boat to reach the camp?
To solve this problem, we can use the concept of relative velocity.
Let's define:
Vw = speed of the boat relative to the water = 9.8 km/h
Vr = speed of the river = 6.0 km/h
D = distance to the fishing camp = 5.2 km
T = time taken to reach the camp.
When the boat is moving upstream, the speed of the boat relative to the ground (Vg) is given by the difference of the boat's speed relative to the water and the speed of the water:
Vg = Vw - Vr
So when the boat is moving upstream, its speed relative to the ground is 9.8 km/h - 6.0 km/h = 3.8 km/h.
Now, we can calculate the time taken to reach the camp using the formula:
Time = Distance / Speed
T = D / Vg
T = 5.2 km / 3.8 km/h
Simplifying:
T = 1.3684 hours
Therefore, it will take approximately 1.37 hours for the boat to reach the fishing camp upstream.