An ocean liner is traveling at 5m/s. A passenger on deck walks towards the rear of the ship at a rate of 4m/s. After walking 30 meters, he turns right and walks at a rate of 4m/s to the rail, which is 12 meters from his turning point.

What is his velocity relative to the water surface while walking to the rear and his velocity while walking toward the rail?

What was his total displacement from his starting point?

Please help me solve this. I do not know how to solve this challenging problem.

To solve this problem, we need to break it down into different stages and calculate the velocities and displacements at each stage. Let's go step by step:

Step 1: The passenger is walking towards the rear of the ship at a rate of 4 m/s. Since the ship is also moving in the same direction at 5 m/s, the relative velocity of the passenger with respect to the water surface would be the difference between the two velocities.

Relative velocity towards the rear = Ship's velocity - Passenger's velocity
Relative velocity towards the rear = 5 m/s - 4 m/s = 1 m/s

Therefore, the passenger's velocity relative to the water surface while walking towards the rear is 1 m/s.

Step 2: After walking 30 meters, the passenger turns right and walks towards the rail at a rate of 4 m/s. At this point, he is no longer walking in the same direction as the ship's movement, so we need to consider this change in direction.

Since the ship's velocity doesn't change, and he is now moving perpendicular to the ship's motion, his velocity relative to the water surface will be the same as his walking speed (4 m/s).

Therefore, the passenger's velocity relative to the water surface while walking towards the rail is 4 m/s.

Step 3: To calculate the total displacement from the starting point, we need to consider the horizontal and vertical components separately.

Horizontal Displacement: The passenger walks 30 meters towards the rear, which is parallel to the ship's motion. Since his relative velocity towards the rear is 1 m/s, the time taken to cover this distance can be calculated as 30 m / 1 m/s = 30 seconds.

Horizontal displacement = Velocity (parallel to the motion) × Time
Horizontal displacement = 5 m/s × 30 s = 150 meters towards the rear

Vertical Displacement: After turning right, the passenger walks towards the rail, which is 12 meters away. Since this displacement is perpendicular to the ship's motion, it does not change due to the ship's velocity.

Vertical displacement = 12 meters

Therefore, the total displacement from the starting point is the vector sum of the horizontal and vertical displacements.

Total displacement = √(Horizontal displacement² + Vertical displacement²)
Total displacement = √(150² + 12²) = √(22500 + 144) = √22644 ≈ 150.44 meters

So, the passenger's total displacement from his starting point is approximately 150.44 meters.

I hope this explanation helps you solve the problem! Let me know if you have any further questions.