A 35 -m-wide river flows in a straight line (the 𝑥 direction) with a speed of 0.25 m/s. A boat is rowed such that it travels directly across the river (along 𝑦). If the boat takes exactly 4 minutes to cross the river, what is the speed of the boat relative to the water?

Answer 1

First, we need to find the distance the boat travels across the river, which can be determined by the time it takes and the speed of the river.

Distance = speed * time
Distance = 0.25 m/s * 240 s (4 minutes = 240 seconds)
Distance = 60 m

Now, we can calculate the speed of the boat relative to the water using the Pythagorean theorem since the boat is moving in a straight line across the river.

Let the speed of the boat be v, then we have:
(35 m)^2 + (60 m)^2 = v^2

1225 m^2 + 3600 m^2 = v^2

4825 m^2 = v^2

v = √4825 m/s
v ≈ 69.5 m/s

Therefore, the speed of the boat relative to the water is approximately 69.5 m/s.