A boat crosses a river of width 174 m in which the current has a uniform speed of 1.13 m/s. The pilot maintains a bearing (i.e., the direc- tion in which the boat points) perpendicular to the river and a throttle setting to give a constant speed of 0.96 m/s relative to the wa- ter.

What is the magnitude of the speed of the boat relative to a stationary shore observer?
Answer in units of m/s.

use Pythagoras to find the resultant

1.13^2 + .96^2 = s^2

To find the magnitude of the speed of the boat relative to a stationary shore observer, we can use vector addition.

Let's break down the velocity of the boat into two components:
1) The component of velocity parallel to the river current
2) The component of velocity perpendicular to the river current

Since the boat is traveling perpendicular to the river current, the component of velocity parallel to the current is 0.
The component of velocity perpendicular to the current is equal to the constant speed of the boat relative to the water, which is 0.96 m/s.

Now, let's consider the velocity of the river current. It has a uniform speed of 1.13 m/s.

To find the magnitude of the speed of the boat relative to the shore observer, we can add the velocities of the boat and the river current together. Since the boat is perpendicular to the river current, we can use Pythagoras' theorem to find the magnitude of the resultant velocity.

Magnitude of the speed of the boat relative to the shore observer = √(velocity of the boat squared + velocity of the river current squared)

= √(0.96^2 + 1.13^2) m/s

Calculating the result, we find:

Magnitude of the speed of the boat relative to the shore observer ≈ 1.47 m/s

Therefore, the magnitude of the speed of the boat relative to a stationary shore observer is approximately 1.47 m/s.