In this particular situation, the resistive force, \( \dot{F}_{R} \), the air exerts on the falling raindrop is given by \( \dot{F}_{R}=-b \dot{v} \), where \( \dot{v} \) is the velocity of the raindrop. b is a constant that depends on the size and shape of the falling object but not its material. f) Determine the numerical value of the constant b in the expression for the air resistance force on the raindrop of this particular situation. \( b= \) g) What if the raindrop is replaced by a plastic pellet of exactly the same shape and size, but with a density, 2.10 times the density of water, what would be the pellet's weight? \( \dot{F}_{g}= \) g) What would be the pellet's terminal velocity? \( \dot{v}_{t}= \) Question Help: D Post to forum

To solve the problem, we need to break it down into parts based on the questions asked. ### Part f: Determine the numerical value of the constant \( b \) The resistive force \( \dot{F}_{R} \) is given by: \[ \dot{F}_{R} = -b \dot{v} \] To find the value of \( b \), we need additional information about the raindrop, such as its size, shape, and the conditions under which the resistive force is measured. If we assume that we have the terminal velocity \( \dot{v}_{t} \) and the weight of the raindrop \( \dot{F}_{g} \), we can set up the equation at terminal velocity where the resistive force equals the weight of the raindrop: \[ \dot{F}_{g} = b \dot{v}_{t} \] If we have values for \( \dot{F}_{g} \) and \( \dot{v}_{t} \), we can rearrange this to find \( b \): \[ b = \frac{\dot{F}_{g}}{\dot{v}_{t}} \] ### Part g: Weight of the plastic pellet The weight of an object is given by the formula: \[ \dot{F}_{g} = \rho V g \] Where: - \( \rho \) is the density of the object, - \( V \) is the volume of the object, - \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)). Given that the density of the plastic pellet is \( 2.10 \) times the density of water, we can express the weight of the pellet as: \[ \dot{F}_{g} = (2.10 \rho_{water}) V g \] ### Part h: Terminal velocity of the plastic pellet The terminal velocity can be found using the same principle as before. At terminal velocity, the weight of the pellet equals the resistive force: \[ \dot{F}_{g} = b \dot{v}_{t} \] Substituting the expression for \( \dot{F}_{g} \): \[ (2.10 \rho_{water}) V g = b \dot{v}_{t} \] From this, we can solve for the terminal velocity \( \dot{v}_{t} \): \[ \dot{v}_{t} = \frac{(2.10 \rho_{water}) V g}{b} \] ### Summary To proceed with the calculations, we need the following: 1. The density of water \( \rho_{water} \) (approximately \( 1000 \, \text{kg/m}^3 \)). 2. The volume \( V \) of the raindrop or pellet. 3. The terminal velocity \( \dot{v}_{t} \) of the raindrop to find \( b \). If you provide the necessary values, I can perform the calculations for \( b \), \( \dot{F}_{g} \), and \( \dot{v}_{t} \).