A person of mass 83.8 kg escapes from a burn- ing building by jumping from a window situ- ated 25 m above a catching net.

The acceleration of gravity is 9.8 m/s2 .
If air resistance exerts a force of 109.1 N on him as he falls, determine his speed just before he hits the net.
Answer in units of m/s

mg = 83.8*9.81 = 822.1 N

so
Fdown = 822.1-109.1 = 713

a = F/m = 713/83.8 = 8.51 m/s^2

v = a t
h = (1/2) a t^2

25 = (1/2)(8.51) (v/8.51)^2

50 (8.51) = v^2

v = 20.6 m/s

To determine the person's speed just before hitting the net, we can use the concept of energy.

First, let's calculate the potential energy of the person when they are 25 m above the catching net. The formula for potential energy is:

Potential Energy = mass * gravity * height

Here, the mass of the person is 83.8 kg, and the height is 25 m. The acceleration due to gravity is 9.8 m/s^2.

Potential Energy = 83.8 kg * 9.8 m/s^2 * 25 m
= 20395 J (joules)

Next, let's take into account the work done by air resistance. The formula for work done is:

Work = force * distance

Here, the force of air resistance is 109.1 N, and the distance is 25 m.

Work = 109.1 N * 25 m
= 2727.5 J

The work done by air resistance is negative since it acts opposite to the direction of motion.

Now, we can calculate the kinetic energy just before hitting the net. The formula for kinetic energy is:

Kinetic Energy = Potential Energy - Work

Kinetic Energy = 20395 J - 2727.5 J
= 17667.5 J (joules)

Finally, we can use the kinetic energy formula to find the speed. The formula for kinetic energy is:

Kinetic Energy = (1/2) * mass * velocity^2

Here, the mass is 83.8 kg, and the kinetic energy is 17667.5 J.

17667.5 J = (1/2) * 83.8 kg * velocity^2

Simplifying:

velocity^2 = (2 * 17667.5 J) / 83.8 kg
velocity^2 = 421.29 m^2/s^2

Taking the square root of both sides:

velocity = √(421.29 m^2/s^2)
velocity ≈ 20.52 m/s

Therefore, the person's speed just before hitting the net is approximately 20.52 m/s.

To determine the person's speed just before hitting the net, we can use the principle of conservation of mechanical energy.

The initial potential energy of the person at the window can be calculated using the formula:

Potential energy = mass × acceleration due to gravity × height

Potential energy = 83.8 kg × 9.8 m/s^2 × 25 m

Next, we need to account for the work done by the air resistance. The work done by air resistance can be calculated using the formula:

Work = force × distance

Work = 109.1 N × 25 m

Now, we can calculate the change in mechanical energy:

Change in mechanical energy = initial potential energy - work

Finally, we can use the principle of conservation of mechanical energy to calculate the person's speed just before hitting the net. The change in mechanical energy is equal to the change in kinetic energy:

Change in mechanical energy = change in kinetic energy

(1/2) × mass × velocity^2 = initial potential energy - work

From this equation, we can solve for the person's velocity.

46 mph