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.
velocity relative to ship+velocityship relative water=velocityrelativeto water.
a.-4+5=1m/s
b. velocity walking across=sqrt(5^2+4^2)
Then how would I find the toatl displacement from starting point?
To solve this problem, we need to break it down into smaller steps. Let's start by finding the passenger's velocity relative to the water surface while walking to the rear of the ship.
Step 1: Determine the velocity of the passenger relative to the ship:
The passenger's velocity relative to the ship is given as 4 m/s.
Step 2: Determine the velocity of the ship:
The ship's velocity is given as 5 m/s.
Step 3: Calculate the passenger's velocity relative to the water surface:
The velocity of the passenger relative to the water surface is the vector sum of their velocity relative to the ship and the ship's velocity. Since the passenger is walking towards the rear of the ship, their velocity relative to the water surface is:
Passenger's velocity relative to the water surface = Passenger's velocity relative to the ship + Ship's velocity
Substituting the given values, we get:
Passenger's velocity relative to the water surface = 4 m/s + 5 m/s = 9 m/s (towards the rear of the ship)
So, the passenger's velocity relative to the water surface while walking to the rear is 9 m/s.
Now, let's find the passenger's velocity while walking toward the rail:
Step 4: Determine the displacement while walking toward the rail:
The passenger walks straight towards the rail, which is 12 meters away from their turning point. Since their velocity is 4 m/s, we can calculate the time taken to reach the rail using the formula:
Time = Distance / Velocity
Time = 12 m / 4 m/s = 3 seconds
Step 5: Determine the velocity of the passenger while walking toward the rail:
The velocity of the passenger while walking toward the rail remains the same at 4 m/s.
Finally, let's calculate the total displacement from the passenger's starting point:
Step 6: Determine the displacement from the starting point:
The passenger walks 30 meters towards the rear of the ship and then turns right. From their turning point, they walk 12 meters towards the rail.
To calculate the total displacement, we need to use trigonometry. The total displacement is the hypotenuse of a right-angled triangle formed by the distances walked in the x and y directions.
Using the Pythagorean theorem, we have:
Total Displacement = √(30^2 + 12^2)
Total Displacement = √(900 + 144)
Total Displacement = √1044
Total Displacement ≈ 32.28 meters
Therefore, the total displacement from the passenger's starting point is approximately 32.28 meters.
To summarize:
- The passenger's velocity relative to the water surface while walking to the rear of the ship is 9 m/s (towards the rear).
- The passenger's velocity while walking toward the rail is 4 m/s.
- The total displacement from the passenger's starting point is approximately 32.28 meters.
I hope this helps! If you have any more questions, feel free to ask.