Rolling ball distance Math problem

In summary, the conversation discusses a math problem involving a ball rolling down an inclined plane. The equation y = .165x^2 + .997x + .845 is provided, where y is the distance traveled and x is the time taken. The goal is to predict the distance traveled in 2 days and discuss any assumptions and limitations of the model. A limitation is mentioned regarding the model not working once the ball reaches terminal velocity. The equation was derived from data collected using a motion sensor. The conversation also touches on the relationship between math and physics and the importance of understanding the underlying physical model for accurate predictions and meaningful coefficients.
  • #1
i_need_help
I have this math problem for school that I need help with

A ball is rolling down an inclined plane. The equation I have is y = .165x^2 + .997x + .845 where y is the distance traveled and x is the time taken

I want to predict the distance it has rolled in 2 days, which I can do

but what sort of assumptions would i have to make?

and what are the strengths and limitations for the model?
for example, a limitation is that when it reaches terminal velocity the model won't work anymore because the model expects the speed to keep increasing

i don't know anything about physics so i need help
 
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  • #2
You need to provide information about your starting equation. You state that x is time, is it seconds, hours, or days? It makes a difference. Can you tell us where your equation came from?
 
  • #3
x is time in seconds

y is distance in metres

the equation came from the data i got from rolling the ball down the slope. i recorded it using a motion sensor, then i came up with a line of best fit for the data. that's my equation
 
  • #4
i_need_help said:
I have this math problem for school that I need help with

A ball is rolling down an inclined plane. The equation I have is y = .165x^2 + .997x + .845 where y is the distance traveled and x is the time taken

I want to predict the distance it has rolled in 2 days, which I can do

but what sort of assumptions would i have to make?

and what are the strengths and limitations for the model?
for example, a limitation is that when it reaches terminal velocity the model won't work anymore because the model expects the speed to keep increasing

i don't know anything about physics so i need help

i_need_help said:
x is time in seconds

y is distance in metres

the equation came from the data i got from rolling the ball down the slope. i recorded it using a motion sensor, then i came up with a line of best fit for the data. that's my equation
Why did you post this in the math section (and title it "Math Problem)? None of those question have any thing to do with mathematics (you did the math part when you derived that equation), they have to do with physics.

I'm going to move this thread to physics homework.
 
  • #5
thank you. i titled it math problem because its for a math assignment...i don't even do physics

but it sort of is more like physics
 
  • #6
Some more questions:
Why did you choose to fit to a quadratic?
How good was your fit?

What physics can do for you is predict the values of, and give meaning to your coefficients. I am surprised that you would be given this problem without the underling physical model.

As far as assumptions go, there is an obvious one concerning length of the ramp required to roll for 2 days.
 

1. How do you calculate the distance of a rolling ball in a math problem?

The distance of a rolling ball can be calculated using the formula d = 0.5 * a * t^2, where d is the distance, a is the acceleration (usually due to gravity), and t is the time the ball has been rolling.

2. What is the difference between a rolling ball and a sliding ball in a math problem?

A rolling ball is one that is in contact with a surface and rotates as it moves, while a sliding ball is one that is in motion without rotation. The distance and speed calculations for a rolling ball will differ from those of a sliding ball due to the rotation involved.

3. How does the angle of the slope affect the distance of a rolling ball in a math problem?

The angle of the slope will affect the acceleration of the rolling ball, which in turn will affect the distance traveled. A steeper slope will result in a greater acceleration and therefore a greater distance traveled.

4. Can you use the same formula to calculate the distance of a rolling ball on different surfaces?

Yes, the formula d = 0.5 * a * t^2 can be used to calculate the distance of a rolling ball on different surfaces as long as the acceleration (a) remains constant. However, the friction and other forces present on different surfaces may affect the acceleration and therefore the distance traveled.

5. How do you take into account the initial velocity of a rolling ball in a math problem?

The initial velocity of a rolling ball can be taken into account by adding it to the formula for distance, resulting in d = v*t + 0.5 * a * t^2, where v is the initial velocity. This will give the total distance traveled by the ball, including the initial velocity.

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