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If a long distance runner with a weight of 596.82 newtons does 35,674.7 joules of work during a portion of a race, what distance will she cover during that portion?

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Sarah06109

Answer:

[tex]\boxed {\boxed {\sf About \ 59.77 \ meters}}[/tex]

Explanation:

Work is equal to the product of force and distance.

[tex]W=F*d[/tex]

We are solving for the distance, d. We know the force is 596.82 Newtons and the work is 35,674.7 Joules.

  • If we convert the units for Joules, the problem will be simpler later.
  • 1 Joule is equal to 1 Newton meter.
  • The work done by the runner, 35,674.7 J, equals 35,674.7 N*m

[tex]F= 596.82 \ N\\W= 35,674.7 \ N*m[/tex]

Substitute the values into the formula.

[tex]35,674.7 \ N*m= 596.82 \ N * d[/tex]

We want to solve for the distance, so we must isolate d on one side of the equation.

d is being multiplied by 596.82 Newtons. The inverse of multiplication is division. Divide both sides of the equation by 596.82 N

[tex]\frac{35,674.7 \ N*m}{596.82 \ N} =\frac{596.82 \ N*d}{596.82 \ N}[/tex]

[tex]\frac{35,674.7 \ N*m}{596.82 \ N}=d[/tex]

The Newtons will cancel, hence the prior unit conversion.

[tex]\frac{35,674.7 \ m}{596.82} =d[/tex]

[tex]59.7746389 \ =d[/tex]

Let's round to the nearest hundredth, so the answer is concise. The 4 in the thousandth place tells us to leave the 7 in the hundredth place.

[tex]59.77 \ m \approx d[/tex]

The distance covered during the portion of the race is about 59.77 meters.

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