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.
see connor's question below
6.40 m/s at an angle 38.66 degrees
To solve this problem, we need to break it down into different parts and calculate the velocities and displacements for each part separately. Let's go step by step:
1. Velocity towards the rear of the ship:
The passenger's velocity relative to the water surface while walking towards the rear of the ship would be the difference between the velocity of the passenger and the velocity of the ship. Given that the ship is traveling at a velocity of 5 m/s and the passenger is traveling at 4 m/s towards the rear, we can calculate the relative velocity as follows:
Relative velocity = Passenger's velocity - Ship's velocity
= 4 m/s - 5 m/s
= -1 m/s (negative sign indicates moving in the opposite direction to the ship)
So, the passenger's velocity relative to the water surface while walking towards the rear is -1 m/s.
2. Velocity towards the rail:
The passenger's velocity relative to the water surface while walking towards the rail would still be the difference between the velocity of the passenger and the velocity of the ship. Since the passenger is turning right and walking towards the rail, the velocity towards the rail will be the same as the ship's velocity of 5 m/s because both are moving in the same direction.
Therefore, the passenger's velocity relative to the water surface while walking towards the rail is 5 m/s.
3. Total displacement:
To calculate the total displacement, we need to consider both the distance traveled towards the rear and towards the rail.
Distance towards the rear: 30 meters
Distance towards the rail: 12 meters
Since the passenger is moving in a straight line towards the rear and then towards the rail, we can use the Pythagorean theorem to find the total displacement:
Total displacement = √[(distance towards the rear)^2 + (distance towards the rail)^2]
= √[(30 m)^2 + (12 m)^2]
= √[900 m^2 + 144 m^2]
= √(1044 m^2)
≈ 32.28 m
So, the passenger's total displacement from his starting point is approximately 32.28 meters.