Terminal velocity

[danny89]

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Question reads: "When two balls are dropped from a tall tower with the same size but ball X has greater mass than ball Y, what is true when both reached terminal velocity?"
Answers: 1. the force of air resistance on either ball is zero
2. ball x has greater velocity
3. ball x has greater acceleration
4. the acceleration of both balls is 9.8 m/s^2
I get there's no acceleration for terminal velocity and they're falling from same height, but why does ball x has greater velocity?
Isn't final velocity depend on square root of 2gh?

 

[MDApplicant3]

the formula using sqrt 2gh is for free fall without a terminal velocity. Since the ball has achieved its terminal velocity mg = air resistance. if i recal correctly, air resistance has the formula bv where b is related to cross sectional area and fluid viscosity and the like. Since the balls are the same we can call b the same in both cases.
so we get Mg = bV, and mg=bv (where capital letters are for the heavier ball)
since M>m, V must be greater than v, since g and b are the same in both cases.

 

[Jepstein30]

the formula using sqrt 2gh is for free fall without a terminal velocity. Since the ball has achieved its terminal velocity mg = air resistance. if i recal correctly, air resistance has the formula bv where b is related to cross sectional area and fluid viscosity and the like. Since the balls are the same we can call b the same in both cases.
so we get Mg = bV, and mg=bv (where capital letters are for the heavier ball)
since M>m, V must be greater than v, since g and b are the same in both cases.

I believe the force of air resistance is kv^2 where k is a constant related to surface area and v is velocity.

Still, though, your reasoning is correct and why the answer is B. There's no need to know much about air resistance on the MCAT. Upward force, balances with mg to reach terminal velocity and how mass plays into it (doesn't change the force but changes the effect of the force.. bigger m = lower a).

for this question, we can also just use real world experience. If I were to drop a paper ball and a metal ball of the same size, we know the metal ball will hit the ground with a greater velocity.

 

[danny89]

Thanks for the help