# A 50.0 kg parachutist jumps out of an airplane at a height of 1.00 km. The parachute opens, and the jumper lands on the ground with a speed of 5.00 m/s. By what amount was the jumper's mechanical energy reduced due to air resistance during this jump?

so, you have to take the inital ME less the final ME, right? And since there is no motion initially the KE=0, and since the jumper is at its terminal velocity, there's no final PE, right? so then would it just be (PE_i - KE_f) or (50kg*9.81m/s^2*1000m)-(.5*50kg*(5^2 m/s))

I think it's incorrect because of the number I keep getting, but I don't know what I'm doing wrong.

(I'm home sick, I'll be here all day... so anytime you could answer this would be fine.)

I would assume the initial KE of the jumper is zero.

Your analysis is correct. Nearly all of the energy is dissipated in the air. Thankfully.

They may be wanting a percentage of energy dissipated, the wording is somewhat ambiguous.

I don't think it's a percentage, we haven't been working with percentages yet in this class.

So it'd be 490500-125?

also, it asks for 'What is the average force of air friction during the jumper's descent if the parachute opened immediately after jumping?' and I'm not sure what equation I could use for that situation.

Ok. Use

average force * distance traveled= energy dissipated.

solve for average force.

## pe=mgh

(50)(9.81)(1000)=491000J

KE=1/2mv^2= (.5)(50)(5)^2=625J

Energy Lost= PE-KE=491000-625= 490375

## To find the average force of air friction during the jumper's descent, you can use the equation:

Average force * distance traveled = energy dissipated

We already calculated the energy dissipated to be 490,375 J, so we can rearrange the equation to solve for the average force:

Average force = energy dissipated / distance traveled

Since the height is 1.00 km, which is equal to 1000 m, the equation becomes:

Average force = 490,375 J / 1000 m

Calculating this, the average force of air friction during the jumper's descent is approximately 490.375 N.

## To find the average force of air friction during the jumper's descent, you can use the equation:

average force * distance traveled = energy dissipated

Since the energy dissipated is equal to the change in mechanical energy, which is given by the difference between the initial potential energy and the final kinetic energy, you can substitute the values in the equation:

average force * distance = (PE_initial - KE_final)

You have already noted that the initial kinetic energy (KE_initial) is zero since there is no initial motion. The final kinetic energy (KE_final) can be calculated using the formula:

KE_final = 0.5 * mass * velocity^2

In this case, the mass of the parachutist is 50.0 kg, and the velocity is given as 5.00 m/s. So you can calculate KE_final as:

KE_final = 0.5 * 50.0 kg * (5.00 m/s)^2

Now, to find the initial potential energy (PE_initial), you can use the formula:

PE_initial = mass * gravity * height

In this case, the mass is 50.0 kg, the acceleration due to gravity is 9.81 m/s^2, and the height is 1.00 km. Be sure to convert the height to meters:

PE_initial = 50.0 kg * 9.81 m/s^2 * 1000 m

Now, plug in the values for PE_initial and KE_final into the equation for average force:

average force * distance = (50.0 kg * 9.81 m/s^2 * 1000 m - 0.5 * 50.0 kg * (5.00 m/s)^2)

Simplify the equation by calculating the values on the right side:

average force * distance = 490,500 J - 125 J

Subtract the values:

average force * distance = 490,375 J

Now, if you know the distance traveled during the descent, divide both sides of the equation by the distance to isolate the average force:

average force = (490,375 J) / distance

Remember to use the correct unit for distance (for example, meters).

By substituting the value for distance, you can calculate the average force of air friction during the jumper's descent.