Question

Calculate the velocity a spherical rain drop would achieve falling from 5.00 km

(a) in the absence of air drag
(b) with air drag. Take the size across of the drop to be 4 mm, the density to be 1.00×10³kg/m³, and the surface area to be πr².

Answer 1

To calculate the velocity of a falling raindrop without air drag, use the formula v = √(2gh). For calculating with air drag, the raindrop's terminal velocity is needed, which cannot be determined without additional information such as the drag coefficient.

Step-by-step explanation:

The student is tasked with calculating the velocity of a spherical raindrop falling from a height of 5.00 km under two different conditions: (a) in the absence of air drag and (b) with air drag. The raindrop has a diameter of 4 mm, a density of 1.00×10³ kg/m³, and the surface area relevant to air drag is given by the formula πr².

(a) In the Absence of Air Drag

To calculate the velocity without air drag, we use the equation of motion for free fall:

v = √(2gh)

where:

v is the final velocity,

g is the acceleration due to gravity (approximately 9.81 m/s²), and

h is the height of fall (5000 m in this case).

Plugging in the values, we get:

v = √(2 * 9.81 m/s² * 5000 m) ≈ 313 m/s

(b) With Air Drag

When considering air drag, the raindrop will eventually reach a terminal velocity where the force due to gravity is equal to the drag force. The terminal velocity can be found using the equation:

v_t = √((2 * mass * g) / (ρ * A * C_d))

However, since we don't have a drag coefficient provided, and calculating terminal velocity with drag is complex and depends on many factors, we acknowledge this part of the problem cannot be solved without additional information such as the drag coefficient.