A lawn roller is pushed across a lawn by a force of 127 N along the direction of the handle, which is 22.5° above the horizontal. If 64.3 W of power is developed for 90.0 s, what distance is the roller pushed?

It is the hor. component of force that moves the roller:

Fh = 127*cos(22.5) = 117.3N.

P = FD / t = 64.3W,
117.3D / 90 = 64.3,
1.3D = 64.3,

D = 64.3 / 1.3 = 49.5m.

To find the distance the roller is pushed, we need to use the formula for work, power, and time.

The formula for work is given by: Work = Force * Distance * cos(theta)

The formula for power is given by: Power = Work / Time

In this case, we know the force (127 N), the power (64.3 W), and the time (90.0 s). We need to determine the distance the roller is pushed.

First, let's rearrange the formula for power to solve for work: Work = Power * Time

Substituting the given values, we get: Work = 64.3 W * 90.0 s = 5797 J

Now let's use this value of work in the formula for work: Work = Force * Distance * cos(theta)

Rearranging the formula for distance, we get: Distance = Work / (Force * cos(theta))

Substituting the given values, we get: Distance = 5797 J / (127 N * cos(22.5°))

Calculating the value of cos(22.5°), we get: cos(22.5°) = 0.9239

Substituting this value back into the formula, we get: Distance = 5797 J / (127 N * 0.9239)

Calculating the distance, we get: Distance = 45.05 meters

Therefore, the roller is pushed a distance of 45.05 meters.