# Terminal Velocity of a Ball Given Velocity and Acceleration

Tags: acceleration, ball, steel, terminal, velocity
 P: 4 1. The problem statement, all variables and given/known data A steel ball is dropped from a great height. When its velocity is 20m/s its acceleration is 7.35 m/s^2. What is it's terminal velocity? 2. Relevant equations V - V_o = at F = ma (Air resistance isn't given, so I don't think drag force can be used.) 3. The attempt at a solution 1. I know the final net force must equal 0. 2. The answer is 40 m/s, but I am unsure of how to get this answer. 3. I tried calculating drag force and taking the limit as time approaches infinity, but I must be making an error.
Emeritus
HW Helper
PF Gold
P: 7,819
 Quote by blradlof 1. The problem statement, all variables and given/known data A steel ball is dropped from a great height. When its velocity is 20m/s its acceleration is 7.35 m/s^2. What is it's terminal velocity? 2. Relevant equations V - V_o = at F = ma (Air resistance isn't given, so I don't think drag force can be used.) 3. The attempt at a solution 1. I know the final net force must equal 0. 2. The answer is 40 m/s, but I am unsure of how to get this answer. 3. I tried calculating drag force and taking the limit as time approaches infinity, but I must be making an error.
How about an assumption such as air resistance is proportional to velocity or perhaps it's proportional to v2 .
 P: 4 Well I know air resistance is proportional to velocity, but I don't see how I can find air resistance without knowing surface area, mass, density, temperature, etc.
Emeritus
HW Helper
PF Gold
P: 7,819
Terminal Velocity of a Ball Given Velocity and Acceleration

 Quote by blradlof Well I know air resistance is proportional to velocity, but I don't see how I can find air resistance without knowing surface area, mass, density, temperature, etc.
bv = mg - ma .

You can find b/m for the given conditions. Then, what does v have to be if a = 0 ?

If so, then I conclude that the air resistance follows a different law .
 P: 4 v = mg/b 1. What does b stand for? 2. I'm sure it is 40 m/s. I came up with multiple answers, but they were all smaller than 40 m/s. 3. They don't give a value for mass. (If I understand what b stands for, I may be able to figure it out.)
 HW Helper Thanks P: 10,754 The forces acting on the falling ball are gravity and air resistance, which is proportional to velocity and opposite to it. Writing up Newton's second law, F=ma=mg-kv. The acceleration is a=g-(k/m) v. You know that a=7.35 m/s2 when v=20 m/s. Plug in: you will find k/m. The ball will reach the terminal velocity when the two forces - gravity and air resistance - cancel, that is, the acceleration is zero: g-(k/m) v=0. You know k/m, how big is v? If the given result is 40 m/s then the air resistance is taken proportional to v2. Do the same procedure, replacing v by v2.
Emeritus
HW Helper
PF Gold
P: 7,819
 Quote by blradlof v = mg/b 1. What does b stand for? 2. I'm sure it is 40 m/s. I came up with multiple answers, but they were all smaller than 40 m/s. 3. They don't give a value for mass. (If I understand what b stands for, I may be able to figure it out.)
b is simply a constant of proportionality.

If you assume that the drag force (air resistance) is proportional to v2, you will get 40 m/s for your answer.

This whole thing is essentially just working with proportiona.
 P: 4 Thank you so much! I forgot that air resistance can be proportional to v and v^2.
 P: 3 a=g-kv, a is a function of veolcity(assumption) k is a constant and then we can find k, by using given data. then find a=0, which kv=g, you can find out v which is terminal veolcity.
Emeritus