A bicycle and its rider together has a mass of 95 kg. What power output of the rider is required to maintain a constant speed of 4.8 m/s (about 10.7 mph) up a 5.0% grade (a road that rises 5.0 m for every 100 m along the pavement)? Assume that frictional losses of energy are negligible.

To find the power output required by the rider to maintain a constant speed up a 5.0% grade, you can follow these steps:

Step 1: Find the force exerted by gravity on the rider and bicycle uphill.
The force exerted by gravity can be calculated using the formula:
Force = mass * acceleration due to gravity
Here, the mass is the combined mass of the rider and bicycle, which is 95 kg. The acceleration due to gravity is approximately 9.8 m/s².
Therefore, the force exerted by gravity on the rider and bicycle uphill is:
Force = 95 kg * 9.8 m/s²

Step 2: Calculate the work done against gravity.
The work done against gravity can be calculated using the formula:
Work = Force * distance
Here, the distance is the vertical distance covered uphill for every 100 m along the pavement. Given that the grade rises 5.0 m for every 100 m, the vertical distance is 5.0 m.
Therefore, the work done against gravity is:
Work = Force * 5.0 m

Step 3: Calculate the power output required by the rider.
The power can be calculated using the formula:
Power = Work / time
In this case, since the speed is constant, the time taken to cover the distance is equal to the distance divided by the speed.
Therefore, the power output required by the rider is:
Power = (Force * 5.0 m) / (100 m / 4.8 m/s)

By plugging in the values into the formulas, you can calculate the required power output of the rider.