Question

A 62kg person escapes from a burning building by jumping from a window 17.5m above the rescue net. Assuming air resistance provides a constant 45N force during the fall, at what speed does the person hit the net?

All work must be shown!!

Answer 1

To find the speed at which the person hits the rescue net, we calculate the net force and use the principle of work and energy. The person hits the net at a speed of approximately 150.9 m/s.

Step-by-step explanation:

To find the speed at which the person hits the rescue net, we need to calculate the net force acting on the person during the fall and then use the principle of work and energy. We can start by calculating the gravitational force acting on the person:

Fg = mg = (62 kg)(9.8 m/s²) = 607.6 N

Next, we can calculate the net force:

Net force = Fg + Fair = 607.6 N + 45 N = 652.6 N

Now, we can use the work-energy principle to find the speed:

W = ΔKE = KEf - KEi

We know the initial kinetic energy is zero because the person is at rest before jumping. The final kinetic energy is given by:

KEf = (1/2)mv²

where m is the mass of the person (62 kg) and v is the final velocity. Rearranging the equation, we get:

v = sqrt(2KEf / m)

Substituting the known values into the equation:

v = sqrt(2(652.6 N)(17.5 m) / (62 kg)) = sqrt(22718.5 m²/s²) ≈ 150.9 m/s

Therefore, the person hits the net at a speed of approximately 150.9 m/s.