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?

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

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, , 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

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

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

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y