Question

A parachutist of mass 50.0 kg jumps out of an airplane at a height of 1000 m. The parachute deploys, and she lands on the ground with a speed of 5.0 m/s. How much energy was lost to air friction during his jump

Answer 1

To solve this problem we will apply the concepts related to energy conservation. For this purpose we have that the energy caused by friction is the difference between the initial and final energy.

$E_f = E_i-E_{friction}$

$E_{friction} = E_i-E_f$

The initial energy is all potential energy, the energy the parachutist has before she actually starts to fall

$E_{initial} = mgh$

Here,

m = mass

g = Acceleration due to gravity

h = Height

$E_{initial} = (50)(9.8)(1000)$

$E_{initial} = 490000J$

The final energy is all kinetic energy, the energy the parachutist as just as she touches the ground is

$E_{final} = \frac{1}{2} mv^2$

Here,

m = Mass

v =Velocity

Replacing,

$E_{final} = \frac{1}{2} (50)(5)^2$

$E_{final} = 625J$

Replacing the values to find the Energy caused by the friction we have that,

$E_{friction} = 490000-625$

$E_{friction} = 489375J$

Answer 2

The amount of energy lost to air friction during the jump is 489375 J.

To calculate the amount of energy lost to air friction, we use the formula below.

Formula:

• E' = (mgh)-mv²/2.............. Equation 1

Where:

• E' = Energy lost due to friction
• m = mass of the parachutist
• h = height of the airplane
• g = acceleration due to gravity
• v = speed .

From the question,

Given:

• m = 50 kg
• h = 1000 m
• v = 5 m/s
• g = 9.8 m/s²

Substitute these values into equation 1

• E' = [(50×1000×9.8)-(50×5²/2)]
• E' = 490000-625
• E' = 489375 J

Hence, The amount of energy lost to air friction during the jump is 489375 J

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