Terminal Velocity of Ice Pellet: Homework Solutions

[JJBlaze]

Homework Statement

An ice pellet drops from a cloud 1.5 km above the Earth's surface. It's spherical so its drag coefficient is 0.45 and it has radius 0.1 mm. The density of air is 1.2 kg/m^3 and the density of ice is 910 kg/m^3.
What is the terminal speed of the ice pellet?
When the pellet is falling at 1% of its terminal speed, what is the magnitude of its acceleration?

Homework Equations

Volume of a sphere= (4/3)(pi)r^3
D=m/v
FD=(1/2)CAP(V^2)

The Attempt at a Solution

I've tried using D=m/v to solve for the mass of the ice pellet. So (910=m/.000418) and then taking this information and rearranging the FD equation to plug into V^2=square root((2 * m * g) / (Cd * r * A). As you move toward terminal velocity FD=w so FD=mg. I used the mass I got and plugged into that to give me FD and then plugged into the FD equation to solve for V^2 but that wasn't it either. I'm not sure what to do since I do not know FD, Velocity or the mass.
Thanks for your help!

 

[SteamKing]

The mass of the pellet should be constant (assuming no melting as it falls). How could you not obtain for the mass knowing the density of ice and the size of the pellet? All else is irrelevant to this calculation.

The drag force is proportional to the square of the velocity, so it's going to change over time until terminal velocity is reached.

To analyze this situation properly, you need to draw a free body diagram of the falling pellet. Then, you've got to apply the equations of linear motion to the problem.

 

[haruspex]

Homework Statement

An ice pellet drops from a cloud 1.5 km above the Earth's surface. It's spherical so its drag coefficient is 0.45 and it has radius 0.1 mm. The density of air is 1.2 kg/m^3 and the density of ice is 910 kg/m^3.
What is the terminal speed of the ice pellet?
When the pellet is falling at 1% of its terminal speed, what is the magnitude of its acceleration?

Homework Equations

Volume of a sphere= (4/3)(pi)r^3
D=m/v
FD=(1/2)CAP(V^2)

The Attempt at a Solution

I've tried using D=m/v to solve for the mass of the ice pellet. So (910=m/.000418) and then taking this information and rearranging the FD equation to plug into V^2=square root((2 * m * g) / (Cd * r * A). As you move toward terminal velocity FD=w so FD=mg. I used the mass I got and plugged into that to give me FD and then plugged into the FD equation to solve for V^2 but that wasn't it either. I'm not sure what to do since I do not know FD, Velocity or the mass.
Thanks for your help!

Pls don't post just a summary of the steps you took. Post the actual working.