Acceleration on incline

[Cole07]

Problem:
Soccer ball released from the top of a smooth incline after 4.58 seconds the ball travels 10 meters 1 second later it has reached the bottom of the incline, the balls acceleration is constant and determine its value
(m/s^2) also need to know the length of the incline
I am posting for the first time and I hope this is ok

Tried to answer by taking 10 meters and dividing by 4.58 seconds but I was told this was wrong with no explanation

To find the incline I would use d= 1/2 a(t)^2

I am just a beginner in Physics and I am definately confused any help would be greatly appreciated to get me on the right path to solving this problem I have tried other expressions to no avail thanks in advance

 

[radou]

The equation of displacement along the incline is, as you stated d = 1/2*a*t^2. Now, you know what distance the ball traveled during the period of 4.58 seconds. Plug these values into the equation, and solve to retrieve the acceleration a. Now, which acceleration is causing a ball roll down an incline? Further on, which component of this acceleration is directed along the incline? You can find the angle of the incline from a simple equation based on these facts.

 

[arildno]

First of all SPLIT up the information neatly, and give names to the quantities you think is relevant!

So, names:
a-acceleration. We know of this it is a constant
d-length of incline
These are the quantities you need to find!

Info:
1. After time $t_{1}=4.58$ seconds, the ball has traveled 10 meters
2. After time $t_{2}=5.58$ seconds, the ball has traveled d meters (reached the end of the incline)

So, what equations to use??

"To find the incline I would use d= 1/2 a(t)^2"

This is perfectly okay!
But remember that that equation has TWO unknown quantities, namely d and a! (the time is known to be 5.58)

But do you agree that you equally well could use the very same equation with 10 meters substituted for d, that is the distance traveled in 4.58 seconds?

 

[Cole07]

ok some of this makes since but i still don't understand if I'm doing the right thing to get the acceleration.

 

[arildno]

Well, let uss use the distance&acceleration of yours when the distance is 10, and time is 4.58!
Plug this in, and you get the equation:
$$10=\frac{1}{2}*a*(4.58)^{2}$$
Do you agree with that?

 

[Cole07]

ok that works great so how do i find how long the incline is now

 

[arildno]

Well, now that you know acceleration "a", how many unknows do you have in your distance formula when the distance is the as yet unkown length of incline?

 

[Cole07]

the distance formula is d=1/2a(t)^2 right

 

[arildno]

Right, so how many unknowns do you have to tackle now?

 

[Cole07]

ok i plugged this into the equation d=1/2*(0.953452451)(4.58)^2 and i get 9.999999997 but the comes up incorrect and it can't be anyway since you know you have already gone 10m isn't this right?

 

[arildno]

But is the time 4.58 when the ball has reached the end of the incline?
Think again!

 

[Cole07]

ok i got it thank you so much you have been a huge help !

 

[arildno]

As you can see, you had most of it inside your head already before I answered you.

I advise you to always start with:
a) defining the quantities you are meeting in a problem
b) note which of these you are supposed to find
c) set up the information&conditions you've been given in a clear manner
and only then:
d) set up the equations you believe can help you solve the problem

Then, go through those equations checking that you have, indeed, gotten all the info you need, and that each of your unknowns appears at least once in those equations/formulae you have set up (otherwise, you won't be able to find that unknown!)

Only after this should you start actually solving your set of equations.