Question

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?

Answer 1

`\boxed {\boxed {\sf About \ 59.77 \ meters}}`

Step-by-step explanation:

Work is equal to the product of force and distance.

`W=F*d`

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

`F= 596.82 \ N\\W= 35,674.7 \ N*m`

Substitute the values into the formula.

`35,674.7 \ N*m= 596.82 \ N * d`

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

`(35,674.7 \ N*m)/(596.82 \ N) =(596.82 \ N*d)/(596.82 \ N)`

`(35,674.7 \ N*m)/(596.82 \ N)=d`

The Newtons will cancel, hence the prior unit conversion.

`(35,674.7 \ m)/(596.82) =d`

`59.7746389 \ =d`

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.

`59.77 \ m \approx d`

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