A person of mass 81.7 kg escapes from a burning building by jumping from a window situated 28.9 m above a catching net.The acceleration of gravity is 9.8 m/s^2.
If air resistance exerts a force of 123.1 N on him as he falls, determine his speed just before he hits the net.
Answer in units of m/s.
To determine the speed of the person just before hitting the net, we can use the principle of conservation of energy. The energy gained by the person while falling should be equal to the potential energy lost. The equation can be written as follows:
Potential Energy Lost = Kinetic Energy Gained
The potential energy lost is given by the formula:
Potential Energy Lost = mass * gravity * height
where
mass = 81.7 kg (given)
gravity = 9.8 m/s^2 (given)
height = 28.9 m (given)
Potential Energy Lost = 81.7 kg * 9.8 m/s^2 * 28.9 m
Next, we need to calculate the kinetic energy gained. The force of air resistance is equal to the work done on the person, which is the force multiplied by the displacement. The equation can be written as follows:
Force of Air Resistance = mass * acceleration
The force is given as 123.1 N (given), and the acceleration is the acceleration due to gravity, which is 9.8 m/s^2 (given).
123.1 N = mass * 9.8 m/s^2
Solving this equation will give us the mass of the person.
mass = 123.1 N / 9.8 m/s^2
Then, we can calculate the kinetic energy gained using the formula:
Kinetic Energy Gained = (1/2) * mass * velocity^2
We can rearrange this equation to solve for velocity:
velocity = sqrt((2 * kinetic energy gained) / mass)
Now we substitute the values we have:
mass = 123.1 N / 9.8 m/s^2
Potential Energy Lost = 81.7 kg * 9.8 m/s^2 * 28.9 m
Finally, we plug the calculated values into the equation for velocity:
velocity = sqrt((2 * Potential Energy Lost) / mass)
After performing the calculations, the speed just before hitting the net is approximately 16.24 m/s.