A kayaker needs to paddle north across a 85-m-wide harbor. The tide is going out, creating a tidal current that flows to the east at 2.0 m/s. The kayaker can paddle with a speed of 3.0 m/s. Find the angle West of North he needs to travel and the time it takes him to cross.

Thanks!

To find the angle the kayaker needs to travel and the time it takes to cross the harbor, we can use vector addition.

Let's break down the velocities involved:

1. The velocity of the tidal current flowing to the east is 2.0 m/s. We'll represent this velocity as V_east.

2. The kayaker's paddling velocity is 3.0 m/s. We'll represent this velocity as V_kayaker.

To find the angle, we need to calculate the resultant velocity vector by adding the vectors V_east and V_kayaker. This can be done using vector addition.

Step 1: Draw a diagram representing the problem with a horizontal line to represent the east direction (along the tidal current) and a vertical line in the north direction.

Step 2: Place V_east (2.0 m/s) on the diagram, pointing to the right (east). Since the kayaker wants to go north, we'll draw V_kayaker (3.0 m/s) pointing straight up (north).

Step 3: Place the vectors head-to-tail: Start the tail of V_east at the origin, and attach the head of V_kayaker to the head of V_east. The resultant vector will go from the tail of V_east to the head of V_kayaker.

Step 4: Draw the resultant vector, representing the kayaker's path, from the tail of V_east to the head of V_kayaker. Mark this vector as V_resultant.

Step 5: Measure the angle between the north direction and V_resultant. This angle represents the angle west of north that the kayaker needs to travel.

To calculate the time it takes the kayaker to cross the harbor, we can divide the width of the harbor (85 m) by the kayaker's velocity (3.0 m/s) in the north direction.

Time = Distance / Velocity
Time = 85 m / 3.0 m/s

Calculating this will give you the time it takes for the kayaker to cross the harbor.

By following these steps, you can find the angle west of north the kayaker needs to travel and the time it takes for them to cross the harbor.

tan-1(2/3)

t = x/v = 85/3