A 50.0-kilogram skydiver jumps from an airplane and is in freefall for 20 seconds. Immediately before she opens her parachute, her kinetic energy is 78,400 joules. If the amount of heat her motion transferred to her surroundings during freefall was 884,000 joules, how far did she fall during her freefall?
(Assume the skydiver's gravitational potential energy is only transformed into heat and kinetic energy, and assume the rate of acceleration due to Earth's gravity is 9.81 m/s/s.)
A. 1,960 meters
B. 1,560 meters
C. 9,620 meters
d = 0.5g*t^2 = 4.9*20^2 = 1960 m.
falling PI conversion= KE at end + Heat
50*g*h=78.4e3 + 88.3e3
compute h
bob is correct
... except he got the wrong exponent in the energy dissipated
henry did not take the dissipated energy into account
To determine how far the skydiver fell during freefall, we need to use the concept of energy conservation. The total mechanical energy of the system remains constant, so we can equate the initial gravitational potential energy to the sum of the final kinetic energy and the heat transferred.
The initial gravitational potential energy (U) can be calculated using the formula:
U = m * g * h,
where m is the mass of the skydiver (50.0 kg), g is the acceleration due to gravity (9.81 m/s^2), and h is the height from which the skydiver jumps.
The final kinetic energy (K) is given as 78,400 joules.
The heat transferred (Q) is given as 884,000 joules.
Using the energy conservation equation:
U = K + Q,
we can rearrange the equation to solve for the height (h) from which the skydiver jumped:
h = (K + Q) / (m * g).
Substituting the given values into the equation:
h = (78,400 J + 884,000 J) / (50.0 kg * 9.81 m/s^2).
Calculating the height (h):
h = 9619.795527 meters.
Therefore, the skydiver fell approximately 9,620 meters during freefall.
The correct answer is C. 9,620 meters.