Answer :
Final answer:
The power of the man riding a cycle up a hill with a velocity of 7.2 km/hr at a slope of 1 in 20 is calculated to be 98 W, taking into account the conversion of velocity units and the vertical component of the velocity due to the slope. The Correct Answer is A
Explanation:
The question asks for the power exerted by a man riding a cycle up a hill with a certain slope and velocity. To calculate the power, we need to consider the work done against gravity and the velocity of the man and the cycle.
First, we will convert the man's velocity from km/hr to m/s:
7.2 km/hr × (⅓ m/s) / (1 km/hr) = 2 m/s.
The slope 1 in 20 means that for every 20 meters of horizontal distance, the elevation increases by 1 meter. The vertical velocity component will be determined by:
2 m/s × (1/20) = 0.1 m/s.
Now, the power required to move up the hill at this speed against gravity can be calculated using the equation for power due to lifting:
Power = Force × Vertical velocity component = (mass × gravity) × vertical velocity.
Substituting the known values we get:
Power = (100 kg × 9.8 m/s²) × 0.1 m/s = 98 W.
Therefore, the power of the man is 98 W, which corresponds to option A.
