Final answer:
Option (c) 700 J. The work done by air resistance on the 5 kg ball falling from a height of 20 m and reaching a speed of 10 m/s is approximately 730 J. The closest answer choice, accounting for potential rounding, is 700 J.
Step-by-step explanation:
To calculate the work done by air resistance, we can use the conservation of energy principle.
The total mechanical energy (sum of potential and kinetic energy) of the ball should be conserved if there were no non-conservative forces like air resistance.
The initial potential energy (Ui) of the ball is its weight (mg) times its height (h), and the final kinetic energy (Kf) is ½mv2 when it acquires a speed v.
So, the work done by air resistance (Wair) is the difference between the initial potential energy and the sum of final kinetic energy and the work done by air resistance:
Ui
= mgh = (5 kg)(9.8 m/s²)(20 m) = 980 J
Kf
= ½mv2
= ½(5 kg)(10 m/s)2
= 250 J
Now, Wair + Kf = Ui
Wair = Ui - Kf
= 980 J - 250 J
= 730 J
Since the value obtained (730 J) is not in the options, the closest option to this value that accounts for possible rounding differences is option (c) 700 J.