A85-kg physics student jumps from a dock into a 135 kg boat that is at rest by the dock. if the velocity
of the student is 4.3 m/s as she leaves the dock, what is the final velocity of the student and the boat?

The final velocity of the student and the boat is 1.66 m/s

Explanation:

Law Of Conservation Of Linear Momentum

The total momentum of a system of bodies is conserved unless an external force is applied to it. The formula for the momentum of a body with mass m and velocity v is P=mv. If we have a system of bodies, then the total momentum is the sum of them all

Let's call the mass of the physics student, the mass of the boat, the initial speed of the student, the initial speed of the boat, the final speed of both, assumed common since they keep joined after the jump. Applying the law of conservation of momentum, being the initial and final momentum of the system, we have

Solving for

The final velocity of the student and the boat is 1.66 m/s

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