Two boats are heading away from shore. Boat 1 heads due north at a speed of 3.7 m/s relative to the shore. Relative to boat 1, boat 2 is moving 35° north of east at a speed of 1.3 m/s. A passenger on boat 2 walks due east across the deck at a speed of 1.2 m/s relative to boat 2. What is the speed of the passenger relative to the shore?

How would i solve this problem I am very confused?

To solve this problem, we need to break it down into smaller steps.

Step 1: Determine the velocity of Boat 2 relative to the shore.
Since we know the speed of Boat 2 (1.3 m/s) and the angle it is moving with respect to the east (35°), we can use trigonometry to find the northward component of Boat 2's velocity relative to the shore. The northward component can be determined using the sine function:
northward component = speed of Boat 2 * sin(angle)
northward component = 1.3 m/s * sin(35°)

Step 2: Determine the velocity of the passenger relative to Boat 2.
Since the passenger is walking due east across the deck of Boat 2 at a speed of 1.2 m/s, the velocity of the passenger relative to Boat 2 is 1.2 m/s in the eastward direction.

Step 3: Combine the velocities of Boat 2 and the passenger.
To find the velocity of the passenger relative to the shore, we need to combine the velocity of Boat 2 relative to the shore (northward component we found in step 1) and the velocity of the passenger relative to Boat 2 (eastward component we found in step 2) using vector addition.

The magnitude of the velocity of the passenger relative to the shore can be determined using the Pythagorean theorem:
velocity of passenger relative to the shore = sqrt((northward component)^2 + (eastward component)^2)

Step 4: Calculate the final answer.
Plug in the values we calculated in steps 1, 2, and 3 into the equation above to find the velocity of the passenger relative to the shore.

By following these steps, you should be able to solve the problem and find the speed of the passenger relative to the shore.