A ferryboat is traveling north with a speed of 5.50 m/s relative to the water. A passenger is walking with a velocity of 2.50 m/s due east relative to the boat. What is the velocity (magnitude only) of the passenger with respect to the water?
To find the velocity of the passenger with respect to the water, we can use vector addition. The velocity of the passenger with respect to the water is the vector sum of the velocity of the passenger relative to the boat and the velocity of the boat relative to the water.
Given:
Velocity of the boat relative to the water = 5.50 m/s (north)
Velocity of the passenger relative to the boat = 2.50 m/s (east)
To find the velocity of the passenger relative to the water, we can use the Pythagorean theorem:
velocity_relative_to_water = √(velocity_relative_to_boat^2 + velocity_relative_to_water^2)
Substituting the given values:
velocity_relative_to_water = √(2.50^2 + 5.50^2)
Calculating:
velocity_relative_to_water = √(6.25 + 30.25)
velocity_relative_to_water = √36.50
velocity_relative_to_water ≈ 6.04 m/s
Therefore, the magnitude of the velocity of the passenger with respect to the water is approximately 6.04 m/s.
To find the velocity of the passenger with respect to the water, we need to combine the velocities of the ferryboat and the passenger.
First, we break the passenger's velocity into its horizontal and vertical components. The horizontal component is 2.50 m/s to the east, and the vertical component is 0 m/s since the passenger is not moving vertically.
Next, we add the horizontal components of the passenger's velocity and the ferryboat's velocity. The ferryboat is moving north, so its horizontal component is 0 m/s.
The resultant horizontal component is 2.50 m/s to the east.
Finally, we find the magnitude of the resultant velocity. Since the passenger's velocity is entirely horizontal, the magnitude of the resultant velocity is simply the magnitude of the horizontal component, which is 2.50 m/s.
Therefore, the velocity (magnitude only) of the passenger with respect to the water is 2.50 m/s.