A boat is rowed due North at 7.0 km/h directly across a river that flows due East at 4.0 km/h. Find the boat's resultant speed.

sqrt(7^2+4^2) is the resultant.

To find the resultant speed of the boat, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, we can consider the boat's velocity due north as one side of the triangle and the river's velocity due east as the other side. The resultant speed (the hypotenuse) can be found by calculating the square root of the sum of the squares of these two velocities.

Let's begin by calculating the magnitude of each velocity. The boat's velocity due north is given to be 7.0 km/h, while the river's velocity due east is given to be 4.0 km/h.

The magnitude of the boat's velocity is 7.0 km/h, and the magnitude of the river's velocity is 4.0 km/h.

Now, let's use the Pythagorean theorem to find the resultant speed. We'll square each magnitude and then take the square root of the sum of the squares.

Resultant speed = √(7.0 km/h)^2 + (4.0 km/h)^2

Simplifying this equation:

Resultant speed = √(49 + 16) km/h

Resultant speed = √(65) km/h

Resultant speed ≈ 8.06 km/h

Therefore, the boat's resultant speed is approximately 8.06 km/h.