Deriving a Launch Angle Equation - Projectile Motion -

In summary, This conversation is about deriving a launch angle equation for a projectile motion lab. The goal of the lab is to hit a moving target with a bullet using a projectile launcher. The equation must use the 5 kinematics equations, but can only consist of dx (range), dy, and h. The equation must also take into account the acceleration (9.8). The conversation discusses different approaches to deriving the equation and what to do next.
  • #1
IntellectIsStrength
51
0
Deriving a Launch Angle Equation -- Projectile Motion -- Please Help

This is physics in the area of projectile motion. My class and I are doing a lab where we have to calculate the launch angle in order to perform a successful lab. The experiment is as follows: the projectile launcher releases a bullet and the goal is to hit the moving target as it falls down (via gravity). In the diagram I provided (in the 2nd attached file), the three circles is the target which in real life will be a thick piece of cardboard.
Now, prior to conducting the lab, we have to derive a launch angle equation. That is, θ = ? something...
We can use the 5 kinematics equations. However, as I've written in the attached files, the equation can only consist (but not necessarily all) of dx (range), dy, and h. Vi, Vf, or ∆t cannot be used (acceleration [9.8] can be used).
As apparent in the first attached file, I have attempted to get to an equation. I started with thinking that, in order for the bullet to hit the target, the vertical distance (dy) of the bullet has to be the same as h-x (where the target will be). Therefore dy= h - x. And ∆dt (distance of target) is what I put for h-x. Hopefully the rest is clear enough to be comprehendable.
I am not at all sure if what I've done is correct. If it is, I'm not quite sure what to do next.

So any help or hints would be greatly, greatly appreciated.

Thanks in advance
 
Last edited:
Physics news on Phys.org
  • #2
I was unable to view your attachments, but by the sound of your project, deriving the equation is not necessary. If you aim at an object, and you fire at the instant the object is released, it will hit the object provided its velocity is great enough. This is a fundamental implication of the way in which you treat projectile motion problems.
 
  • #3
Deriving an equation is necessary... we have to do it. And you can't arbitrarily release the bullet, the angle has to be calculated.

Here are the images:

http://img379.imageshack.us/img379/1393/phsy13ag.jpg [Broken]
http://img323.imageshack.us/img323/1853/untitled5po.png [Broken]
 
Last edited by a moderator:
  • #4
Back to top!
 
  • #5
The vertical component of both the target and bullet are the same, they will fall at the same rate as long as they are released at the same time, so why is there any question to what angle is required to hit the object?

After t seconds, the bullet and target will have fallen the same distance vertically, the only difference is that the bullet could have moved horizontally closer to the target.

If the bullet is fired as the target is dropped, an angle of 0 is needed to hit the target. How? Because the equation for the y displacement of an object in relation to the time and vertical component of velocity is the same for both objects, since the component of x velocity and x distance has no bearing on the change in y.

---
I'm not entirely sure what the question is. If they're released at the same time, what does he want?

y=vy(t) -.5gt²
If both objects are to meet each other, there y distance would be the same, right?
so, y1=the vertical displacement of the bullet after t seconds
y2=the vertical displacement of the target after t seconds.
Since they are to meet, the vertical displacement of the two objects must be equal. The target has no angle about it, it drops straight down.
y1=y2
-or-
vsinθ-.5gt²=vsin0-.5gt²

θ=0°


What exactly is the question you're asking...
 
Last edited:
  • #6
The following methodology almost never fails.

1. Construct free body diagrams of relevant objects

2. Write equations of motion of relevant objects in convenient coordinate systems. In this case there should be 3:

[tex](1): \ y_1 = f_1(\theta,t)[/tex] ...projectile
[tex](2): \ x_1 = f_2(\theta,t)[/tex] ...projectile
[tex](3): \ y_2 = f_3(t)[/tex] ...target

3. Articulate what you want to know/do. In this case
[tex]- \ eliminate \ t \ from \ the \ equations[/tex]
[tex]- \ find \ \theta \ needed \ for \ the \ projectile \ to \ hit \ the \ target[/tex]

4. Use what you know to get what you want
- one of the 3 equations allows t to be elimiated from the other equations
- the other 2 should relate y1, y2, and theta. Be careful how you relate y1 and y2 to each other. Net result is that you should be able solve theta in terms of known parameters
 
Last edited:

1. What is a launch angle equation?

A launch angle equation is a mathematical formula that helps calculate the angle at which an object must be launched to achieve a desired distance or height. It takes into account factors such as the initial velocity, acceleration due to gravity, and the angle of launch.

2. How is a launch angle equation derived?

A launch angle equation is derived using principles of projectile motion, which involves analyzing the motion of an object moving through the air under the influence of gravity. By applying equations of motion and trigonometry, a launch angle equation can be determined.

3. What is the importance of a launch angle equation?

A launch angle equation is important because it allows us to predict the trajectory of a projectile and determine the best angle to launch it for a desired outcome. This is useful in a variety of fields, such as sports, engineering, and physics.

4. What factors affect the launch angle?

The launch angle is affected by several factors, including the initial velocity, acceleration due to gravity, and air resistance. Other factors that may impact the launch angle include the shape and weight of the object being launched and the surface it is being launched from.

5. Can a launch angle equation be applied to all types of projectiles?

Yes, a launch angle equation can be applied to all types of projectiles, as long as they are subject to the same forces of motion, such as gravity and air resistance. This includes objects like baseballs, rockets, and even satellites.

Similar threads

  • Introductory Physics Homework Help
Replies
7
Views
2K
  • Introductory Physics Homework Help
2
Replies
36
Views
2K
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
15
Views
20K
  • Introductory Physics Homework Help
2
Replies
39
Views
2K
  • Introductory Physics Homework Help
Replies
8
Views
1K
  • Introductory Physics Homework Help
Replies
15
Views
7K
  • Introductory Physics Homework Help
Replies
8
Views
2K
  • Introductory Physics Homework Help
Replies
8
Views
1K
  • Introductory Physics Homework Help
Replies
17
Views
12K
Back
Top