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?

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.