A man cycles up a hill whose slope is 1in20. If themass of the man and the cycle is 150kg and the man covers a distance of 100m along the incline, calculate the work done by theman.

sinα=1/20=0.05

sinα=h/s => h=s•sinα
W=ΔPE=m•g•h=(m₁+m₂)•g•s•sinα=..

To calculate the work done by the man while cycling up the hill, we need to use the formula:

Work = Force * Distance * cosθ

Here's how to calculate it step by step:

1. Calculate the force exerted by the man against gravity:
Force = mass * acceleration due to gravity = 150 kg * 9.8 m/s²

2. Calculate the angle of the hill slope:
Slope = 1 in 20 = 1/20 = 0.05
Angle (θ) = arctan(0.05)

3. Convert the angle from radians to degrees (optional):
Angle in degrees = θ * (180/π)

4. Calculate the distance along the incline:
Given distance = 100 m

5. Calculate the cosine of the angle:
cosθ = cos(angle in radians)

Now, plug in the values into the work formula:

Work = Force * Distance * cosθ

Simply substitute the values we calculated into the formula and solve for work:

Work = (150 kg * 9.8 m/s²) * 100 m * cosθ

After substituting, you'll have the work done by the man while cycling up the hill.