Projectile Motion Lab: Calculating Projectile Trajectory with a Slingshot

[Byrgg]

We did an experiment, where we used a slingshot to launch a clay ball and then we had to calculate various things, like the time of the trip, the max height, etc., knowing the horizontal displacement, as well as the angle at which the ball was fired(and the vertical displacement, but that's pretty much just common sense, seeing as the ball was about level with the ground).

First off, I don't think my answers were accurate, sure, in a human experiment, there's always going to be at least a little bit of error, but my final answer seems way off. Here's the data gathered:

average horizontal displacement: 1.69m
angle at which the ball was fired: tan(theta) = y/x = 22/14 = 58 degrees
vertical displacement: 0m

The first thing I calculated was the initial vertical velocity, and I got 5.77m/s, then, using the angle at which the projectile was fired along with this, I got the initial velocity, 6.80m/s [58 degrees above the horizontal].

Following this, I calculated the the initial horizontal velocity, and got 3.60m/s.

I then got the flight time, which was 0.47s.

Finally, I got the max height, 1.08m. This doesn't seem right at all, and the time is probably off by a fair bit. The calculations obtained a result of over 1m, and yet, in the experiment, the ball didn't even seem to go higher than about half a metre. Could someone tell me if I did something wrong, or if it's just that all of the little sources of error contributed to one final answer that was way off?

Also, my physics teacher said something which confused me. Since or slingshots were propped up on books, I asked him if we take this into account for the y displacement. He said it really didn't matter too much, as the books didn't change things very much. He then mentioned something about the errors being even smaller if the angle was lower, how is this so? I'm wondering how a lower initial angle of the trajectory would result in a lesser amount of error in the y displacement.

 

[member 553083]

It sounds like you may have made a mistake in your calculations, as the results you got seem to be far too large for what you measured in the experiment. The most likely cause of this discrepancy is that you did not take into account air resistance, which will cause the ball to slow down and fall to the ground earlier than it would if it were in a vacuum. Air resistance will also reduce the maximum height of the ball, as it will reduce the amount of energy it has to reach its peak height. Your teacher is right that the angle of the launch will affect the amount of error. A lower angle will result in less error because it reduces the time the ball is in the air, meaning that any errors due to air resistance will be less significant.