A tugboat exerts a constant force of 5.00 × 10^3 N on a ship moving at constant speed through a harbor. How much work does the tugboat do on the ship if each moves a distance of 3.00 km?

The work done by a force is given by the equation:

Work = Force x Distance x cos(θ)

where:

• Force is the magnitude of the force,
• Distance is the distance over which the force is applied, and
• θ is the angle between the force and the direction of motion.

In this case, the force is 5.00 × 10^3 N, the distance is 3.00 km (or 3.00 x 10^3 m, because we need the distance in meters to match the units of the force in newtons), and the angle is 0 degrees (because the force and the motion are in the same direction).

So, the work done by the tugboat on the ship is:

Work = (5.00 × 10^3 N) x (3.00 x 10^3 m) x cos(0)

The cosine of 0 degrees is 1, so:

Work = (5.00 × 10^3 N) x (3.00 x 10^3 m) x 1

Work = 15.00 x 10^6 N.m

Work = 15.00 x 10^6 Joules

So, the tugboat does 15.00 x 10^6 Joules of work on the ship.

The work done by a force is given by the equation:

Work = Force x Distance x cos(θ)

where:

• Force is the magnitude of the force,
• Distance is the distance over which the force is applied, and
• θ is the angle between the force and the direction of motion.

In this case, the force is 5.00 × 10^3 N, the distance is 3.00 km (or 3.00 x 10^3 m, because we need the distance in meters to match the units of the force in newtons), and the angle is 0 degrees (because the force and the motion are in the same direction).

So, the work done by the tugboat on the ship is:

Work = (5.00 × 10^3 N) x (3.00 x 10^3 m) x cos(0)

Since the cosine of 0 degrees is 1, this simplifies to:

Work = (5.00 × 10^3 N) x (3.00 x 10^3 m) x 1

So, the work done by the tugboat on the ship is 1.50 x 10^7 Joules.