Question

A cyclist in a race must climb a 5° hill at a speed of 8 m/s. If the mass of the bike and the biker together is 80 kg, what must be the power output of the biker to achieve the goal?

(a) 640 W
(b) 320 W
(c) 160 W
(d) 80 W

Answer 1

To calculate the power output of the biker, we need to consider the work done by the biker to climb the hill. The power output must be 640 W.

Step-by-step explanation:

To calculate the power output of the biker, we need to consider the work done by the biker to climb the hill. The work done is given by the equation:

Work = Force x Distance x Cos(angle)

In this case, the force is the weight of the biker and the bike, which is the mass multiplied by the acceleration due to gravity. The distance is the height of the hill.

Plugging in the values:

Work = (80 kg x 9.8 m/s²) x (height xsin(5°)) = 80 x 9.8 x (height x 0.087)

Since power is defined as the work done divided by the time taken:

Power = Work / Time

Plugging in the given value of speed:

8 m/s = work / time

Solving for work and substituting the value:

work = 640 W

Therefore, the power output of the biker must be 640 W. Hence, the correct option is (a) 640 W.