# Parabolic motion (experiment)

We performed a laboratory, performing six releases of a sphere with angles $15^\circ,30^\circ,45^\circ,60^\circ,75^\circ,40^\circ$ a parabolic movement, took five distances for each angle, the initial velocity was calculated $3.025~\text{m/s}$. Then doing 5 tosses of the sphere with an angle of $90^\circ$ times were recorded and calculated initial velocity was $3.33~\text{m/s}$, the question is: Why are these speeds almost the same?

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Can you describe by what mechanism you launch the balls? Also, why are you surprised that the experimental speeds are roughly the same? – Keep these mind Apr 23 '13 at 19:31
Launcher is a launcher device with a spring mechanism the speed was the same for both releases, the question is because an angle of 90 with that speed is greater than the average of all other angles? – Mauricio Apr 23 '13 at 19:41
Height or total time should both be fine, although determining height precisely is probably easier than timing (unless you have some sophisticated apparatus). How did you measure time? – Keep these mind Apr 23 '13 at 19:48
with a chronometer ... – Mauricio Apr 23 '13 at 19:53
I that case, it might be that you started the chronometer a little too soon, or stopped it a little too late? Could that be? If you have the formula for the $90^\circ$ launch, you could work out by how much imprecision there may be in the timing. – Keep these mind Apr 23 '13 at 19:59

## 2 Answers

I can think of two or three things.

1. The whole experiment can be divided into two parts. In one part you calculate the initial speed by measuring distance. In the other part you calculate speed by measuring time. Assuming that your calculations are correct, that would suggest that there might be a difference in the accuracy of measuring distance and measuring time. Assuming that distance is more accurate than time, you can actually work out what the time should have been. You do this by plugging $3.025~\text{m/s}$ into the formula for the $90^\circ$ launch. This will give you the time you would have expected. Compare that to the actual time, by taking the difference, and see if that would be reasonable. (Google for "human reaction time", and see how it compares.)

2. Since the time for $90^\circ$ is somewhat longer than expected, you must make sure that you didn't start your chronometer too soon. I haven't seen this experiment, and don't know if it makes a difference, but the chronometer should not be started at the moment of release of the spring (by the hand), but rather a bit later, at the moment of release of the ball (by the spring).

3. I assume that the release point of the ball is on the same height as the landing plane. If your spring is sitting on top of the landing plane, then the release point will be slightly higher than the plane. In that case, all your formulas would need to be modified to include that difference.

PS: It is a bit awkward to respond since I can't see the experimental set-up in a diagram. If you have a link to a precise picture, that would be great.

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I'm a little confused by one part of your question. You ask,

Why are these speeds almost the same?

If you are asking why they are almost the same, and not completely different, then the answer is that you expect them to be the same because they are caused by the same launch mechanism. But I don't think you are asking that.

I think you are asking why they are almost the same and not exactly the same. The answer is that you can't see that they are different until you take the uncertainties into account. You don't report the uncertainties, but my guess is that the uncertainty for the second part is much larger than the uncertainty for the first part. And my guess is that the two numbers are within the uncertainties of your experiment.

I agree with Gugg that you should check to see what time you should have in the second part. I solved for the intial speed in terms of the measured time for that part of the experiment, and I got that an error of $0.1 \mathrm{s}$ in the time will produce an error of $9.8 \mathrm{m/s}$ in the speed. So the difference you see in the speeds suggests that you are over-estimating the time by about $0.03 \mathrm{s}$ in that second part. That is actually smaller than normal human reaction time, so I would guess that your two values are well within the uncertainty you have in the experiment.

If you still have the apparatus, you might try repeating one of the angles from the first set of experiments, and measure both the time and the range. You could then compare the speed you get from those measurements to see how well they agree. In this case, you know for certain that the speed is the same (because it's the same launch), so any disagreement is due to the measurements themselves.

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