Answer
(a) The total work done on the stunt woman is $3445~J$
(b) The work done by gravity is $4961~J$
(c) The work done by air resistance is $-1516~J$
(d) The average force of air resistance is $187 ~N$
Work Step by Step
(a) We can find the stunt woman's change in kinetic energy:
$\frac{1}{2}mv^2 = \frac{1}{2}(62.5~kg)(10.5~m/s)^2 = 3445~J$
The total work done on the stunt woman is $3445~J$
(b) We can find the work done by gravity:
$W_g = mgh = (62.5~kg)(9.80~m/s^2)(8.10~m) = 4961~J$
The work done by gravity is $4961~J$
(c) We can find the work $W_a$ done by air resistance:
$Work = 3445~J$
$W_a+W_g = 3445~J$
$W_a = 3445~J-W_g$
$W_a = 3445~J-4961~J$
$W_a = -1516~J$
The work done by air resistance is $-1516~J$
(d) We can use the magnitude of the work done by air resistance to find the average force of air resistance:
$F~d = W_a$
$F = \frac{W_a}{d}$
$F = \frac{1516~J}{8.10~m}$
$F = 187~N$
The average force of air resistance is $187 ~N$.
