a gardener pushes a mower a distance of 900m in mowing a yard. the handle of the mower makes an angle of 40.0 degrees with the ground. the gardener exerts a force of 35.0 N alonf the handle of the mower. how much work does the gardener do in mowing the lawn?

Fp = 35*cos40 = 26.8 N. = Force parallel to yard.

Work = Fp*d = 26.8 * 900 = 24,130 Joules

To calculate the work done by the gardener in mowing the lawn, we can use the formula:

Work = Force x Distance x cos(theta)

Where:
- Work is the work done (in joules)
- Force is the force exerted by the gardener (in newtons)
- Distance is the distance covered (in meters)
- theta is the angle between the force and the direction of motion (in degrees)

Given:
Force = 35.0 N
Distance = 900 m
theta = 40.0 degrees

First, we need to convert the angle from degrees to radians:
theta_rad = theta * (pi / 180)

Next, we can substitute the given values into the formula:
Work = 35.0 N * 900 m * cos(40.0 degrees)

Finally, we can calculate the work:
Work ≈ 35.0 N * 900 m * cos(40.0 degrees) ≈ 27,387.78 joules

Therefore, the gardener does approximately 27,387.78 joules of work in mowing the lawn.

To find the work done by the gardener in mowing the lawn, we need to calculate the work done by the force exerted along the handle of the mower.

The formula to calculate work is given by:

Work = Force * Distance * Cos(theta)

Where:
- Force is the magnitude of the force exerted along the handle of the mower, which is 35.0 N.
- Distance is the distance covered by the gardener while mowing the yard, which is 900 m.
- Cos(theta) is the cosine of the angle between the direction of the force and the displacement.

In this case, the angle between the handle of the mower and the ground is 40.0 degrees. Since the force is exerted along the handle, the angle between the force and the displacement is the same, which is 40.0 degrees.

Now, let's calculate the work done:

Work = 35.0 N * 900 m * cos(40.0 degrees)

To find the cosine of 40.0 degrees, we can use a scientific calculator or calculator app.

Work ≈ 35.0 N * 900 m * 0.7660

Now, we calculate the product of these values:

Work ≈ 23,985 J

Therefore, the gardener does approximately 23,985 Joules of work in mowing the lawn.