Hi, I'm doing a PH3 paper right now and I'm doing a graph. It's about a marble falling off a table at speed. We measured the distance (x) in the test and now we know the avarage. But in the question it says you should also add x2 (squared) in our table. Does this mean we have to square the avarage distances for every height?

Yes, I think so. If you square the distance that the marble lands from the edge of the table (I assume that's what your 'x' value is) and plot this x^2 value against the height of the table you should get a linear relationship.

thank you! But then how do I get k from the formula x2 (squared)=k h ? My gradient is 142

If x^2 = kh, then k=\frac {x^2}h. You have data for x and h, so see what values of k they produce.

If x^2 = kh, then k=\frac {x^2}h. You have data for x and h, so see what values of k they produce.

Isn't k supposed to be constant though? The same for every one? Plus it says 'giving your reasoning'

Yes, k should be the same (or close to it) for each h,x pair of data. Why do you think that might be? Hint: how is the time that it takes for the marble to fall vertically and hit the floor related to the height of the table?

Yes, k should be the same (or close to it) for each h,x pair of data. Why do you think that might be? Hint: how is the time that it takes for the marble to fall vertically and hit the floor related to the height of the table?

So do I just do k for all of them and get the avarage? Is it to do with distance=timexspeed?

Yuo said yuo were plotting a graoh, so for each value of h on the horizontal axis you should plt the value for x^2 on the vertical axis. have yuo done that? Are you able to pliot an almost straight line for all yuor data points? If so, then the value for k is constant.

Yuo ask if this has to do with distance = time x speed. That relationship works only of there is no acceleration. For the horizontal component of the marble's motion its horozaontal speed is constant, so the distance x depends only on the amount of time the marble is in the air. But for the vertical component of motion velocity is not constant (when you drop something it picks up speed as it falls). The result is that if you double the height of the table it takes less than twice as much time for the marble to hit the floor - it actuially takes sqrt(2) times as long. You must raise the table by a factor of 4 in order to double the time it takes to fall, so in your experiment if you raise the table by a factor of 4 the distance the marble travels horizontally is doubled. Is that what your data shows?