A

Step 1: Calculate the gravitational potential energy (PE) at the height of 1 km (1000 m).
Using the formula for gravitational potential energy:
$$ PE = mgh $$
where
- $m = 0.001$ kg (mass of the drop),
- $g = 9.81$ m/s$^2$ (acceleration due to gravity),
- $h = 1000$ m (height).
Substituting the values:
$$ PE = 0.001 imes 9.81 imes 1000 = 9.81 ext{ J} $$

Step 2: Calculate the kinetic energy (KE) just before it hits the ground.
Using the formula for kinetic energy:
$$ KE = \frac{1}{2}mv^2 $$
where
- $v = 50.0$ m/s (velocity just before impact).
Substituting the values:
$$ KE = \frac{1}{2} imes 0.001 imes (50.0)^2 = 1.25 ext{ J} $$

Step 3: Use the work-energy principle to find the work done by the resistive force (W_resistive).
The work done by the resistive force can be found by the difference in potential energy and kinetic energy:
$$ W_{resistive} = PE - KE $$
Substituting the values:
$$ W_{resistive} = 9.81 - 1.25 = 8.56 ext{ J} $$

Therefore, the work done by the unknown resistive force is approximately 8.56 J.