Question

Rachel and Andrew are riding on a ferry boat traveling east at 3.5 m/s. Rachel rolls a marble with a velocity of 0.95 m/s north, straight across the deck of the boat to Andrew. What is the velocity of the marble relative to the water?

Answer 1

The velocity of the marble relative to the water is 3.63 m/s

Step-by-step explanation:

The information given are;

The velocity of the ferry relative to the water = 3.5 m/s

Direction of motion of the ferry = East

The velocity of the marble (on the ferry) relative to the ferry = 0.95 m/s

The direction of the marble = North

The (resultant) velocity of the marble relative to the water,
`v_R`, is found as follows;

Resolution of the velocities;

Velocity of the ferry = 3.5·i + 0·j

Velocity of the marble = 0·i + 0.95·j

`v_R` = Combined (resultant) velocity = √(3.5² + 0.95²) = 3.63 m/s

The velocity of the marble relative to the water = 3.63 m/s.