Final answer:
The speed a raindrop would achieve falling from 5.00 km without air drag is 98 m/s. However, the speed with air drag cannot be determined with the given information.
Step-by-step explanation:
When a raindrop falls from a certain height, it gains speed due to the force of gravity. The speed a spherical raindrop would achieve falling from 5.00 km can be calculated using the formula:
a) In the absence of air drag: v = sqrt(2 * g * h), where v is the speed, g is the acceleration due to gravity (9.8 m/s^2), and h is the height (5.00 km or 5000 m). Plugging in the values, we get: v = sqrt(2 * 9.8 * 5000) = 98 m/s.
b) With air drag: The presence of air drag affects the speed of the falling raindrop. The drag force is given by: F = (1/2) * ρ * A * C * v2, where F is the drag force, ρ is the density of the fluid (1.00 × 10³ kg/m³), A is the cross-section area facing the fluid (π * r2), C is the drag coefficient, and v is the velocity. At terminal velocity, the drag force equals the gravitational force, which gives us: (1/2) * ρ * A * C * v2 = m * g, where m is the mass of the raindrop. From this equation, we can solve for v to find the terminal velocity with air drag. However, since the size across the drop is given (4 mm), we cannot directly find the terminal velocity using the given information. Additional information is needed, such as the shape of the drop or the drag coefficient. Therefore, the speed with air drag cannot be determined with the given data.