Final answer:
To determine the biker's power output for ascending a 5% hill at 10 m/s, calculate the work against gravity based on the biker's mass and the hill's slope, then divide by time to find power as work done per second.
Step-by-step explanation:
The power output necessary for a biker to climb a 5% hill at a speed of 10 m/s, while having a mass of 69 kg, can be found by calculating the work done against gravity and then determining the power needed to do this work at the given speed.
The work done against gravity (W) is W = mgh, where m is the mass, g is the acceleration due to gravity (9.8 m/s2), and h is the height gained. The height gained per second (h) can be found by multiplying the vertical speed component by the time, considering the hill's angle and biker's speed. The power output (P) is P = W/t, where t is the time, which is 1 second in this case since we are calculating power per second. Assuming a 5% incline translates to a 5 m vertical rise for every 100 m of horizontal travel, we use trigonometry to find h per second, and then use this to calculate power.