# Find Mass of Object in Kings Dominion's Drop Zone Ride | Formula & Solution

• suwarna07
In summary, the conversation is about a physics problem involving an object's motion in a ride at an amusement park called "King's Dominion". The problem requires finding the mass of the object, and the equations used involve acceleration, air resistance, and velocity. There is a discrepancy about the validity of one of the equations used and whether it takes into account the variable acceleration caused by air resistance. The conversation also includes a discussion about the level of difficulty of the problem and whether it involves calculus or not.

## Homework Statement

Its the drop zone in kings dominion

d = 82.9 m
initial velocity = 0
final velocity (before the brakes are applied) = 32.19 m/s
i know there is gravity downward and airresistance upward.
I need to find the mass of the object.

## Homework Equations

First i found the acceleration using

v12= v02 + at

a = 6.25 m/s2

And i am confused since air resistance is directly proportional to objects velocity. Is the acceleration i found is the final acceleration before the brakes are applied or is it the average acceleration.

## The Attempt at a Solution

I need to find the mass but i can't think of any way to start.

Any help is appreciated

At first, I had NO idea what you were talking about (because I don't live in Virginia). You need to communicate a little better. Anyway...

suwarna07 said:

## Homework Equations

First i found the acceleration using

v12= v02 + at

Well, this equation is totally wrong, but I'm assuming that you meant to write:

because based on the number you got for the acceleration, this seems to be the equation that you used.

suwarna07 said:
And i am confused since air resistance is directly proportional to objects velocity. Is the acceleration i found is the final acceleration before the brakes are applied or is it the average acceleration.

It might be neither -- it might just be completely wrong. Here is the problem: the equation I wrote above is valid ONLY for motion with CONSTANT acceleration. If you are going to model the drag as being proportional to velocity, then the object's acceleration will NOT be constant, because the force acting on it will not be constant. There is a way to solve this problem and figure out the object's motion. However it requires solving a differential equation (something from calculus). Do you know how to do this?

cepheid said:
At first, I had NO idea what you were talking about (because I don't live in Virginia). You need to communicate a little better. Anyway...

Well, this equation is totally wrong, but I'm assuming that you meant to write:

yea i put the wrong equation. sorry about that. and i thought everyone knows drop zone so didnt try to be too specific.

Anyway, i haven't learned calculus based physics
So, what i did is completely wrong?
Or if there is any other way to find the objects mass then it would be helpful too

"King's Dominion" is an amusement park roughly half way between Washington, D. C. and Richmond, Virginia (not the most informative title for the thread). "The drop zone" is a ride in which people are literaly dropped a fair distance.

Suwarna07, none of the formulas you suggest depend upon mass so you could not possibly "solve" them for mass. It might be the case that the "drag" force was dependent upon both velocity and mass but you would have to propose a formula for such a force before you could use it.

The air resistance depends on the size of object ... (not mass but volume occupied!) that is,,, if two spheres of same volume but masses m and 2m are in free fall, force due to air is same for both.

So you can take it a constant F(air) for your calculation,
just take F(earth) downward and F(air) upward and equate it to mass times net acceleration!

also ... F(air) don't depend on weight of object but you can still write F(air) = m x a(air)

But yes this will only help you find acc due to air, mass gets canclelled.

I'll think of something else and get back on this

cupid.callin,

I agree that the drag force depends on the physical size of the object. Unfortunately, this is not all that it depends on. As the original poster, HallsofIvy, and I have all alluded to, the drag force also depends on the velocity of the object. Common models that I have seen are like:

Fair = C*v

OR

Fair = C*v2

where C is some constant that depends upon the radius of the object, the drag coefficient, etc. In other words, the drag force increases with increasing velocity (until the terminal velocity is reached, assuming there is time for that to happen). So, the drag force is NOT constant, which makes this problem mathematically harder to solve.

which level question is this?
then at least we can know what things we have to keep in mind before solving the problem

cupid.callin said:
which level question is this?
then at least we can know what things we have to keep in mind before solving the problem

its high school non-calculus based physics

so cepheid this question must not be involving any calculus(as suwarna07 said) or dealing with variable accleration ...
there must be a little something we all are missing ...

## 1. What is Kings Dominion?

Kings Dominion is a theme park located in Doswell, Virginia. It opened in 1975 and features over 60 rides, including 12 roller coasters, as well as a water park and live entertainment.

## 2. How many roller coasters does Kings Dominion have?

Kings Dominion currently has 12 roller coasters, including the iconic Intimidator 305, which reaches speeds of up to 90 miles per hour.

## 3. Is Kings Dominion suitable for all ages?

Yes, Kings Dominion offers a variety of rides and attractions for all ages. The park has a designated children's area, as well as thrill rides for older guests.

## 4. Can I bring outside food and drinks into Kings Dominion?

No, outside food and drinks are not permitted inside the park. However, there are numerous dining options available within the park.

## 5. Does Kings Dominion have any special events or festivals?

Yes, Kings Dominion hosts various special events and festivals throughout the year, including Halloween Haunt and WinterFest. These events offer unique experiences and themed attractions.