Relationship between Launch height and range of a projectile

[Stanley_physics]

Homework Statement

In a practical that we conducted, we were investigating the relationship between Launch height and the range (horizontal distance it travels) of a projectile. We launched a projectile from various heights and measured the horizontal range it traveled before reaching the ground. We concluded that as height increases, range also increases. We are now trying to explain why an increase in launch means an increase in range.

2. The attempt at a solution
This is our attempt at explaining why this occurs.

"The results suggest that an increase in launch height causes an increase in range, as was predicted in the hypothesise. This relation can be linked directly to the physics concepts of projectile motion. Range depends upon two factors, horizontal velocity and air time of the projectile. Since velocity was constant throughout the investigation, the only factor that had an impact upon the range is air time. Increasing the height means that the projectile has a greater vertical distance to travel. The upwards motion of the projectile is unchanged regardless of the height, however the difference in range between each height occurs due to the increased or decreased downwards distance the projectile must travel which is the result of the launch height. Increasing the launch height increases the downward distance, giving the horizontal component of the velocity greater time to act upon the projectile and hence increasing the range. "

Also, we derived an equation for range (S) in terms of height (h).

S = (vcostheta(vsintheta + (v^2sin^2theta-2gh)^1/2)/-g

where v = initial velocity, theta = launch angle, and g=gravity

This is the equation in terms of the values that we got in our practical. v = 2.94 , theta = 45 degrees, g = -9.8

therefore , S = (2.94cos45)(2.94^2(sin45)^2-2(-9.8)(h))^1/2)/-(-9.8)

This maybe useful.

We were looking for a more scientific explanation which could maybe include mathematical explanations as well, however we could not create one ourselves. We couldn't find anything worthwhile on the internet either. It will be really useful if someone can help us out.

 

[mfb]

I think the explanation is fine. You can simplify it, however: Neglecting things like the air density changing with height (irrelevant at your parameters), increasing the launch height is equivalent to lowering the floor. The mass will always have the same horizontal distance when it crosses the height of the launch point again. Afterwards it continues to travel forwards, and the more height it has at this point (the lower the floor is relative to this point) the more it will travel forwards before hitting the ground.

 

[kuruman]

I agree with the assessment by @mfb. However, I feel obliged to make a remark involving good habits that will serve you well in the future, especially when you draw and label force diagrams. Think of g as the magnitude of the acceleration of gravity, that is g = +9.8 m/s². For projectile motion you start with the general equation for constant vertical acceleration y(t) = y₀ + v_0y t +(½)a_y t² and then adapt it tot he specific problem. Here, y₀ = h, v_0y t = v₀sin(θ) and a_y = -g. Therefore, y(t) = y₀ + v₀sin(θ) t - (½)g t² where g is a positive quantity. Note how the component of the acceleration a_y is given a negative algebraic sign indicating that the direction is "down". No more negative signs need to be introduced as you proceed with the algebra and, when the time comes to substitute numbers, you replace g with +9.8 m/s².

 

[rias2]

Homework Statement

In a practical that we conducted, we were investigating the relationship between Launch height and the range (horizontal distance it travels) of a projectile. We launched a projectile from various heights and measured the horizontal range it traveled before reaching the ground. We concluded that as height increases, range also increases. We are now trying to explain why an increase in launch means an increase in range.

2. The attempt at a solution
This is our attempt at explaining why this occurs.

"The results suggest that an increase in launch height causes an increase in range, as was predicted in the hypothesise. This relation can be linked directly to the physics concepts of projectile motion. Range depends upon two factors, horizontal velocity and air time of the projectile. Since velocity was constant throughout the investigation, the only factor that had an impact upon the range is air time. Increasing the height means that the projectile has a greater vertical distance to travel. The upwards motion of the projectile is unchanged regardless of the height, however the difference in range between each height occurs due to the increased or decreased downwards distance the projectile must travel which is the result of the launch height. Increasing the launch height increases the downward distance, giving the horizontal component of the velocity greater time to act upon the projectile and hence increasing the range. "

Also, we derived an equation for range (S) in terms of height (h).

S = (vcostheta(vsintheta + (v^2sin^2theta-2gh)^1/2)/-g

where v = initial velocity, theta = launch angle, and g=gravity

This is the equation in terms of the values that we got in our practical. v = 2.94 , theta = 45 degrees, g = -9.8

therefore , S = (2.94cos45)(2.94^2(sin45)^2-2(-9.8)(h))^1/2)/-(-9.8)

This maybe useful.

We were looking for a more scientific explanation which could maybe include mathematical explanations as well, however we could not create one ourselves. We couldn't find anything worthwhile on the internet either. It will be really useful if someone can help us out.

Hi!

Just wondering where you got your sources from. I'm trying to conduct the same experiment and I need some background citations.

Thanks!

 

[haruspex]

Hi!

Just wondering where you got your sources from. I'm trying to conduct the same experiment and I need some background citations.

Thanks!

The thread is nearly three years old, Stanley_physics is no longer a member, and I see no evidence that he used any sources.

 

[juicebox_441]

Hi!

Just wondering where you got your sources from. I'm trying to conduct the same experiment and I need some background citations.

Thanks!

Hi there!
I am also currently conducting the same experiment, and was wondering if you have gathered citations? If you could, will you be able to please link them? I am now in your shoes lol (you're not pressured !
Thanks

 

[hmmm27]

The thread is over three years old. The previous poster from two months ago - who wanted somebody else to do their homework prep for them - hasn't been around in a month. Is this a generational thing ? Please start your own thread, telling us what you have done, and where you're stuck.

 

[rias2]

Hi there!
I am also currently conducting the same experiment, and was wondering if you have gathered citations? If you could, will you be able to please link them? I am now in your shoes lol (you're not pressured !
Thanks

Hey! I actually did find some sources, although not very good ones. Unfortunately, I only have them in APA format, I'm sorry! 4.3 projectile motion – university Physics Volume 1. (2019). Retrieved February 12, 2021

Brown, R. (1992, September 01). Maximizing the range of a projectile. Retrieved February 12, 2021

Disabled World. (2020, October 07). Average height to Weight Chart: Babies to teenagers. Retrieved February 12, 2021

Henelsmith, N. (2016, May 12). Projectile Motion: Finding the Optimal Launch Height. Retrieved 2021.

Lucas, S. (2009). What affects the range of a projectile? Retrieved February 12, 2021

Srivastava, A. (2015, May). An Experiment On Projectile Motion. Retrieved 2021.

Vinopal, L. (2017, November 03). Harvard researchers Confirm optimal way to throw stuff. Retrieved February 18, 2021

 

[rias2]

The thread is over three years old. The previous poster from two months ago - who wanted somebody else to do their homework prep for them - hasn't been around in a month. Is this a generational thing ? Please start your own thread, telling us what you have done, and where you're stuck.

Haha actually, I was desperately trying to find sources for my experiment after looking for about a week! Please don't assume things you couldn't possibly know about:)

 

[hmmm27]

Haha actually, I was desperately trying to find sources for my experiment after looking for about a week! Please don't assume things you couldn't possibly know about:)

From the original post, the assignment consisted of trying to find out - by experiment - if there is a relation of launch height to range. Makes me wonder why you need citations in the first place, for bog standard kinematics equations.

Also, one of your cites :

Disabled World. (2020, October 07). Average height to Weight Chart: Babies to teenagers. Retrieved February 12, 2021

seems to be worth commenting on : spherical objects work best for (basic) projectile motion experiments.

 

[rias2]

From the original post, the assignment consisted of trying to find out - by experiment - if there is a relation of launch height to range. Makes me wonder why you need citations in the first place, for bog standard kinematics equations.

Also, one of your cites :

Disabled World. (2020, October 07). Average height to Weight Chart: Babies to teenagers. Retrieved February 12, 2021

seems to be worth commenting on : spherical objects work best for (basic) projectile motion experiments.

It’s actually for my sports exercise and health class! I was trying to find the average height for an adolescent, as I was measuring the correlation between human launch height and projectile range. I’m not sure how you conduct your experiments for school, but here, we do background research before we experiment:)

 

[hmmm27]

I still think you'd do better starting with cannonballs, before moving up to human test subjects : the aerodynamics is pretty different over long distances.

 

[rias2]

I still think you'd do better starting with cannonballs, before moving up to human test subjects : the aerodynamics is pretty different over long distances.

Unfortunately, it is a sports health class so I have to test human subjects rather than tools.

 

[hmmm27]

Ah well, there's no accounting for taste, then. High school physics says the best angle is 45deg. Aerodrag says that's wrong and it's less than that. Aerodrag is right, but requires working knowledge of the drag properties of the object to know just how right.

Since your class isn't actually physics and presumably your looking for formulae/tables to integrate rather than practice, I'd again suggest a new thread ; either in the 'Physics' or 'Medical' subforums - depending on whether you need more help with kinematics or kinaesthetics - rather than dry-humping an old, only partially related thread.

[Edit: that'd be 'Physics : Classical Physics' subforum]

 

[rias2]

Ah well, there's no accounting for taste, then. High school physics says the best angle is 45deg. Aerodrag says that's wrong and it's less than that. Aerodrag is right, but requires working knowledge of the drag properties of the object to know just how right.

Since your class isn't actually physics and presumably your looking for formulae/tables to integrate rather than practice, I'd again suggest a new thread ; either in the 'Physics' or 'Medical' subforums - depending on whether you need more help with kinematics or kinaesthetics - rather than dry-humping an old, only partially related thread. Ta

[Edit: that'd be 'Physics : Classical Physics' forum]

Nope! This thread was absolutely fine and definitely did help me. I was just responding, so I could help somebody else. Bye!

 

[juicebox_441]

Hey! I actually did find some sources, although not very good ones. Unfortunately, I only have them in APA format, I'm sorry!4.3 projectile motion – university Physics Volume 1. (2019). Retrieved February 12, 2021

Brown, R. (1992, September 01). Maximizing the range of a projectile. Retrieved February 12, 2021

Disabled World. (2020, October 07). Average height to Weight Chart: Babies to teenagers. Retrieved February 12, 2021

Henelsmith, N. (2016, May 12). Projectile Motion: Finding the Optimal Launch Height. Retrieved 2021.

Lucas, S. (2009). What affects the range of a projectile? Retrieved February 12, 2021

Srivastava, A. (2015, May). An Experiment On Projectile Motion. Retrieved 2021.

Vinopal, L. (2017, November 03). Harvard researchers Confirm optimal way to throw stuff. Retrieved February 18, 2021

Thank you soooo much! I also found some other sources, but my teacher required "a wide variety of sources" so I was wondering if you had any- and you did!
Have a great day and stay safe,
Cheers!