A sailboat weighing 980 lb with its occupants is running...

A sailboat weighing 980 lb with its occupants is running downwind at $8 \mathrm{mi} / \mathrm{h}$ when its spinnaker is raised to increase its speed. Determine the net force provided by the spinnaker over the $10-\mathrm{s}$ interval that it takes for the boat to reach a speed of $12 \mathrm{mi} / \mathrm{h}$.

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Key Concepts

Newton's Second Law of Motion

Newton's Second Law states that the net force on an object is equal to the product of its mass and its acceleration. This principle is fundamental in mechanics and is used to calculate the force required to change an object's velocity over time.

Impulse-Momentum Theorem

The impulse-momentum theorem links the net force applied over a time interval to the change in momentum of an object. It asserts that the impulse (force multiplied by the time interval) equals the change in momentum (mass times the change in velocity), providing an alternative method to compute net force.

Acceleration

Acceleration is the measure of how quickly an object's velocity changes over time. In problems where a speed change is specified within a given time interval, determining the acceleration is a crucial step before applying force calculations.

Unit Conversion

Unit conversion is vital in mechanics to maintain consistency across measurements. Converting quantities such as speed from miles per hour to feet per second, or translating weight in pounds into mass, ensures that the application of formulas like F = m × a is done correctly with compatible units.

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