## Need help with calculating initial velocity of a projectile!

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chunglin94
Posts: 4
Joined: Thu Apr 28, 2011 7:36 am

### Need help with calculating initial velocity of a projectile!

Hey guys.
I have conducted an experiment on water rockets for my physics IB assignment. My objective is to see how angles would affect horizontal range.
I have encountered a situation where my school does not have a device to measure the initial velocity of the projectile motion. So, i have done my experiment and now is expected to write a "predicted" results. I do not have the initial velocity, and now i have no idea how to do my "predicted" results.

My attempt to solve this problem:
Since i Have done my experiment, i have the range and angle. From there, i calculate my initial velocity using the formula : Square root (Rg/ sin2 (theta) . Now, my initial velocity shows this ....
22.82
30.28
20.65
19.9
28.78
18.06
17.37
16.86
16.34
15.92
15.58
15.37
15.01
14.73
14.36
14.37
14.74
All these are different so which one should i use to calculate my "predicted result" for the range of a projectile????

bfollinprm
Posts: 1203
Joined: Sat Nov 07, 2009 11:44 am

### Re: Need help with calculating initial velocity of a projectile!

chunglin94 wrote:Hey guys.
I have conducted an experiment on water rockets for my physics IB assignment. My objective is to see how angles would affect horizontal range.
I have encountered a situation where my school does not have a device to measure the initial velocity of the projectile motion. So, i have done my experiment and now is expected to write a "predicted" results. I do not have the initial velocity, and now i have no idea how to do my "predicted" results.

My attempt to solve this problem:
Since i Have done my experiment, i have the range and angle. From there, i calculate my initial velocity using the formula : Square root (Rg/ sin2 (theta) . Now, my initial velocity shows this ....
22.82
30.28
20.65
19.9
28.78
18.06
17.37
16.86
16.34
15.92
15.58
15.37
15.01
14.73
14.36
14.37
14.74
All these are different so which one should i use to calculate my "predicted result" for the range of a projectile????
Familiar with a mean and standard deviation? To first order the answer is $$\overline{velocity} \pm \sigma_{velocity}$$. Really, though, this should be done with a $$\chi^{2}$$ test of constancy (1 degree of freedom (mean)) over the function velocity = f(angle) to see if the naive $$v= \sqrt{R/sin(2\theta)}$$ is a good approximation (since it ignores wind resistance, etc).
Last edited by bfollinprm on Thu Apr 28, 2011 10:54 am, edited 1 time in total.

chunglin94
Posts: 4
Joined: Thu Apr 28, 2011 7:36 am

### Re: Need help with calculating initial velocity of a projectile!

Sorry i'm confused. Can you simply put it in a easier way so that i can follow?

bfollinprm
Posts: 1203
Joined: Sat Nov 07, 2009 11:44 am

### Re: Need help with calculating initial velocity of a projectile!

chunglin94 wrote:Sorry i'm confused. Can you simply put it in a easier way so that i can follow?
Just take the average, and find the standard deviation. A quick look through your textbook should tell you how to do both. It's all that can be expected from a high school physics class, but just so you know it's a bit of a lie (you can't average things unless you performed the EXACT SAME experiment over and over again, but you didn't; you changed the angle).

If you could, give me the angle that goes with each velocity, and I'll show you what I mean.

chunglin94
Posts: 4
Joined: Thu Apr 28, 2011 7:36 am

### Re: Need help with calculating initial velocity of a projectile!

okay these are the angles, the initial velocity for these angles have already been posted. They are in order
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85

bfollinprm
Posts: 1203
Joined: Sat Nov 07, 2009 11:44 am

### Re: Need help with calculating initial velocity of a projectile!

This chart shows the velocities as a function of angle. The straight line represents the average of all the velocities. As you can see, there's a clear quadratic trend (curved line) that better fits the points. This represents air resistance. Of course, a 3rd degree polynomial would do even better, and a 5th degree even better, but at some point the model gets really complicated, and we're just fitting noise, not physics. Think of it this way: There's a bunch of little things you can do with your bottle rocket to affect its flight that isn't changing the angle. You probably did a lot of these things without noticing. There are also some things, like air resistance, you would want your model to include. You need a statistical tool to measure whether or not what you're fitting is actual physics (air resistance) or just noise (experimental error on your part). That statistical tool is called the chi^2 test, but you probably don't have to worry about it. Instead, use the mean and pretend that the velocity(angle) function is a straight line (even though it obviously isnt).

So why is the function actually quadratic? Well, the time you spend in the air is greater for larger angles. so, there's more time for air to slow the rocket. Since that means that the initial velocity slows due to something other than gravity (a quadratic effect), it makes it seem like there's a slower initial velocity for high theta than there actually is. For some trials you obviously hit an updraft in flight, which kept the rocket up longer (these are outliers and should actually be excluded). To avoid these errors you should run the experiment with the same angle multiple times (>20 for statistical purposes) and average these points together, using the scatter (standard deviation) as an error bar for each angle, use the chi^2 test to correct for the quadratic effect, and then average the points using a weighted average based on the scatter of each point.
Last edited by bfollinprm on Thu Apr 28, 2011 1:50 pm, edited 1 time in total.

chunglin94
Posts: 4
Joined: Thu Apr 28, 2011 7:36 am

### Re: Need help with calculating initial velocity of a projectile!

bfollinprm wrote:

This chart shows the velocities as a function of angle. The straight line represents the average of all the velocities. As you can see, there's a clear quadratic trend (curved line) that better fits the points. This represents air resistance. Of course, a 3rd degree polynomial would do even better, and a 5th degree even better, but at some point the model gets really complicated, and we're just fitting noise, not physics. Think of it this way: There's a bunch of little things you can do with your bottle rocket to affect its flight that isn't changing the angle. You probably did a lot of these things without noticing. There are also some things, like air resistance, you would want your model to include. You need a statistical tool to measure whether or not what you're fitting is actual physics (air resistance) or just noise (experimental error on your part). That statistical tool is called the chi^2 test, but you probably don't have to worry about it. Instead, use the mean and pretend that the velocity(angle) function is a straight line (even though it obviously isnt).

So why is the function actually quadratic? Well, the time you spend in the air is greater for larger angles. so, there's more time for air to slow the rocket. Since that means that the initial velocity slows due to something other than gravity (a quadratic effect), it makes it seem like there's a slower initial velocity for high theta than there actually is. For some trials you obviously hit an updraft in flight, which kept the rocket up longer (these are outliers and should actually be excluded). To avoid these errors you should run the experiment with the same angle multiple times (>20 for statistical purposes) and average these points together, using the scatter (standard deviation) as an error bar for each angle, use the chi^2 test to correct for the quadratic effect, and then average the points using a weighted average based on the scatter of each point.
HI thanks for your advice. First thing, i can't see the image that you put in. How would you graph this function? I get what you mean but the most important thing that I need at the moment is to make a good assumption of the initial velocity. Perhaps you can give me a quick guide of the graphing method?

Thank you

HappyQuark
Posts: 762
Joined: Thu Apr 16, 2009 2:08 am

### Re: Need help with calculating initial velocity of a projectile!

chunglin94 wrote:Sorry i'm confused. Can you simply put it in a easier way so that i can follow?
I didn't know bfollinprm had any patients!

grae313
Posts: 2297
Joined: Tue May 29, 2007 8:46 pm

### Re: Need help with calculating initial velocity of a projectile!

chunglin94 wrote: First thing, i can't see the image that you put in.
Here you go:

bfollinprm
Posts: 1203
Joined: Sat Nov 07, 2009 11:44 am

### Re: Need help with calculating initial velocity of a projectile!

chunglin94 wrote:
bfollinprm wrote:

This chart shows the velocities as a function of angle. The straight line represents the average of all the velocities. As you can see, there's a clear quadratic trend (curved line) that better fits the points. This represents air resistance. Of course, a 3rd degree polynomial would do even better, and a 5th degree even better, but at some point the model gets really complicated, and we're just fitting noise, not physics. Think of it this way: There's a bunch of little things you can do with your bottle rocket to affect its flight that isn't changing the angle. You probably did a lot of these things without noticing. There are also some things, like air resistance, you would want your model to include. You need a statistical tool to measure whether or not what you're fitting is actual physics (air resistance) or just noise (experimental error on your part). That statistical tool is called the chi^2 test, but you probably don't have to worry about it. Instead, use the mean and pretend that the velocity(angle) function is a straight line (even though it obviously isnt).

So why is the function actually quadratic? Well, the time you spend in the air is greater for larger angles. so, there's more time for air to slow the rocket. Since that means that the initial velocity slows due to something other than gravity (a quadratic effect), it makes it seem like there's a slower initial velocity for high theta than there actually is. For some trials you obviously hit an updraft in flight, which kept the rocket up longer (these are outliers and should actually be excluded). To avoid these errors you should run the experiment with the same angle multiple times (>20 for statistical purposes) and average these points together, using the scatter (standard deviation) as an error bar for each angle, use the chi^2 test to correct for the quadratic effect, and then average the points using a weighted average based on the scatter of each point.
HI thanks for your advice. First thing, i can't see the image that you put in. How would you graph this function? I get what you mean but the most important thing that I need at the moment is to make a good assumption of the initial velocity. Perhaps you can give me a quick guide of the graphing method?

Thank you
I used excel. there are good guides all around google: http://tinyurl.com/42tavm8. What you really want is the average (arithmetic mean) and standard deviation of your velocity measurements. Pick up your algebra II textbook, it's probably chapter 11.