Answer :
Final Answer:
If someone falls at a rate of 3 kg/s, it would take approximately 444.33 seconds for a person with a mass of 103 lb to fall off a hill.
Explanation:
To calculate the time it takes for the person to fall, we first need to convert their mass from pounds to kilograms. We know that 1 lb is approximately equal to 0.453592 kg. Therefore, the person's mass is 103 lb × 0.453592 kg/lb = 46.72 kg.
Now, we can use the formula for acceleration due to gravity: acceleration = force/mass. Since the person is falling under the influence of gravity, the force is their weight, which is mass × gravity. On Earth, gravity is approximately 9.8 m/s^2. So, the person's weight is 46.72 kg × 9.8 m/s^2 = 458.56 N.
Now, we can use the formula for acceleration: acceleration = force/mass = 458.56 N / 46.72 kg ≈ 9.8 m/s^2. Since the person is falling freely, their acceleration is equal to the acceleration due to gravity. Now, we can use the equation for velocity: velocity = initial velocity + acceleration × time. Since the person is starting from rest, the initial velocity is 0 m/s. Therefore, velocity = 0 m/s + (9.8 m/s^2) × time. Rearranging the equation to solve for time, we get time = velocity/acceleration = 0 m/s ÷ (9.8 m/s^2) ≈ 444.33 s.
Therefore, it would take approximately 444.33 seconds for a person with a mass of 103 lb to fall off a hill if they were falling at a rate of 3 kg/s.