# B Ranges of Projectiles With and Without Drag

#### ProfuselyQuarky

Gold Member
I recently completed a lab using an online projectile simulator about the range of projectiles. I launched a projectile with different initial speeds (5 m/s, 10 m/s, 15 m/s, 20 m/s, and 25 m/s). For each trial, I did the launch with and without air resistance and I plotted Range (with Air Resistance) vs. Initial Speed and Range (without Air Resistance) vs. Initial Speed onto my calculator. The former graph was logarithmic and the latter graph was exponential. Why is this so? This has nothing to do with my homework; I just wanted to know.

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#### Khashishi

Exponential, you say?

The case without air resistance is easy to calculate. Go ahead and do that, and see if it agrees with the simulator. Maybe the simulator is wrong.

#### ProfuselyQuarky

Gold Member
Exponential, you say?

The case without air resistance is easy to calculate. Go ahead and do that, and see if it agrees with the simulator. Maybe the simulator is wrong.
What do you mean "calculate"? What would you like me to calculate?

EDIT: All I want to know is why one of the graphs is logarithmic while the other is exponential.

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#### SteamKing

Staff Emeritus
Homework Helper
What do you mean "calculate"? What would you like me to calculate?
Calculate the range of the projectile, both with and without considering the effect of drag or air resistance.

The equations of projectile motion neglecting air resistance are used quite a bit in intro. physics courses. If you go to the HW forums here at PF for Intro Physics, you'll see that users have quite a few questions where projectile motion is discussed without considering air resistance. Not so many questions, however, assuming that air resistance cannot be neglected.

#### mathman

The range will be strongly dependent on initial direction.

#### ProfuselyQuarky

Gold Member
Calculate the range of the projectile, both with and without considering the effect of drag or air resistance.

The equations of projectile motion neglecting air resistance are used quite a bit in intro. physics courses. If you go to the HW forums here at PF for Intro Physics, you'll see that users have quite a few questions where projectile motion is discussed without considering air resistance. Not so many questions, however, assuming that air resistance cannot be neglected.
Yes, obviously, the range of a projectile is shortened when drag is accounted for. I know how to use a variation of the kinematic equations to calculate that sort of stuff without regard for drag, but I'm not so sure what to do with the air resistance. The drag coefficient used was 1 and the altitude was set to 0 . . .
The range will be strongly dependent on initial direction.
The initial angle was 80 degrees. The simulator did not give an option on actual direction. I designed the experiment so that the only variables were the initial velocities and the range itself.

#### Khashishi

80 degrees to the horizon or the zenith?

I don't think you are expected to analytically calculate the range with air resistance, but you should be able to calculate it without air resistance, even in a starting physics class. Compare that to the simulation to test out the simulation, and then form some conclusions about the air resistance case.

#### SteamKing

Staff Emeritus
Homework Helper
Yes, obviously, the range of a projectile is shortened when drag is accounted for. I know how to use a variation of the kinematic equations to calculate that sort of stuff without regard for drag, but I'm not so sure what to do with the air resistance. The drag coefficient used was 1 and the altitude was set to 0 . . .

The initial angle was 80 degrees. The simulator did not give an option on actual direction. I designed the experiment so that the only variables were the initial velocities and the range itself.
For the purposes of range calculations, drag and air resistance are the same thing: the amount of drag is proportional to the speed of the projectile, usually to the second power.

The following article shows how the range of a projectile is affected when air resistance or drag varies as the speed of the projectile, rather than the square of the speed:

http://farside.ph.utexas.edu/teaching/336k/Newtonhtml/node29.html

#### ProfuselyQuarky

Gold Member
80 degrees to the horizon or the zenith?
Ah, I'm guessing zenith? The angle only determined the angle in which the projectile was launched.
I don't think you are expected to analytically calculate the range with air resistance, but you should be able to calculate it without air resistance, even in a starting physics class. Compare that to the simulation to test out the simulation, and then form some conclusions about the air resistance case.
Yeah, I know. I already did all that. For this specific assignment, I was the one who was creating the data analysis questions to be answered. This entire thread is because of curiosity. I guess that the Range (without Air Resistance) vs. Initial Speed graph was exponential because the range of the projectile increased at a faster pace compared to the Range (with Air Resistance) vs. Initial Speed. I wish there was some way to show you my graphs/charts/sample calculations.
For the purposes of range calculations, drag and air resistance are the same thing: the amount of drag is proportional to the speed of the projectile, usually to the second power.
I actually thought that drag and air resistance were synonymous terms always . . .
The following article shows how the range of a projectile is affected when air resistance or drag varies as the speed of the projectile, rather than the square of the speed:

http://farside.ph.utexas.edu/teaching/336k/Newtonhtml/node29.html
Thank you for the article. I’ll look at it in depth, but right now, by just skimming through, it looks like something that I am capable of doing.

#### nasu

Ah, I'm guessing zenith? The angle only determined the angle in which the projectile was launched.
The angle determines the range in a significant way.
For a given initial speed, the range can be anywhere from zero to some maximum values, depending on the angle.

#### ProfuselyQuarky

Gold Member
The angle determines the range in a significant way.
For a given initial speed, the range can be anywhere from zero to some maximum values, depending on the angle.
Okay, so what would be the difference between "80 degrees to the horizon or the zenith"?

#### Khashishi

In other words, is it pointing almost straight up, or pointing just above level with the ground? You said 80 degrees, but that is ambiguous.

#### ProfuselyQuarky

Gold Member
In other words, is it pointing almost straight up, or pointing just above level with the ground? You said 80 degrees, but that is ambiguous.
80 degrees meaning almost straight up—10 degrees off from being a straight 90 degree angle upward.

"Ranges of Projectiles With and Without Drag"

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