A 75 kg person escapes from a burning building by jumping from a window 25 m above a catching net. Assuming that air resistance exerts a 95 N force on the person during the fall, determine the person's velocity just before hitting the net.

My main problem is finding the force of the person... do you take 9.81*75 and minus 95 to get the downward force of the person?

ok, thanks. I think I'm on the right track.

Yes. The force down is mg minus air resistance.

Yes, you are on the right track. To determine the downward force acting on the person, you need to subtract the force of air resistance from the weight of the person. The weight of the person can be calculated by multiplying the mass (75 kg) by the acceleration due to gravity (9.81 m/s^2), so the weight is 75 kg * 9.81 m/s^2 = 736.5 N.

Now, to find the net force acting on the person, you subtract the force of air resistance (95 N) from the weight (736.5 N):

Net Force = Weight - Force of Air Resistance
Net Force = 736.5 N - 95 N
Net Force = 641.5 N

The net force represents the force accelerating the person downward. Now let's use this net force to find the person's velocity just before hitting the net.

To do this, we can use the equation:

Net Force = Mass * Acceleration

In this case, the net force is 641.5 N and the mass of the person is 75 kg. We need to find the acceleration. Rearranging the equation, we get:

Acceleration = Net Force / Mass
Acceleration = 641.5 N / 75 kg
Acceleration ≈ 8.5533 m/s^2

Now, we can use this acceleration to find the final velocity of the person using the following equation of motion:

Final Velocity^2 = Initial Velocity^2 + 2 * Acceleration * Displacement

The initial velocity is zero since the person starts from rest, the acceleration is 8.5533 m/s^2, and the displacement is 25 m (height of the jump). Rearranging the equation, we get:

Final Velocity^2 = 2 * Acceleration * Displacement
Final Velocity^2 = 2 * 8.5533 m/s^2 * 25 m
Final Velocity^2 ≈ 428.33 m^2/s^2

Finally, we take the square root of both sides to find the final velocity:

Final Velocity ≈ √428.33 m^2/s^2
Final Velocity ≈ 20.7 m/s

Therefore, the person's velocity just before hitting the net is approximately 20.7 m/s.