Master Projectile Graphing: How to Plot Displacement vs. Theta

[lukus09]

i know how to plot horizontal dispacement (x axis) against vertical displacement (y axis) but i want to plot displacement (x axis) vs theta (y axis)?

 

[Gib Z]

For a single given theta, the displacement still varies over time. Perhaps you mean total range?

If you want to plot Range on the x-axis and angle of projection on the y axis, first you have to find an equation that relates them.

 

[lukus09]

For a single given theta, the displacement still varies over time. Perhaps you mean total range?

If you want to plot Range on the x-axis and angle of projection on the y axis, first you have to find an equation that relates them.

yes i mean total range, can anyone help me out? so basically I am looking foir an equation for total range of a projectile with drag

 

[lukus09]

For a single given theta, the displacement still varies over time. Perhaps you mean total range?

If you want to plot Range on the x-axis and angle of projection on the y axis, first you have to find an equation that relates them.

yes i mean total range, can anyone help me out? so basically I am looking foir an equation for total range of a projectile with drag

 

[Gib Z]

Well do you know how to model a projectile in 1 dimension with drag? If you do, the two dimensional case can be solved by simply considering the horizontal and vertical motions separately.

 

[Gib Z]

Okay in response to the personal message, you have no done drag, although you have done projectile motion in a vaccum. Now I'm guessing I am safe in assuming that this was projectile motion in 2 dimensions, but I now need to know, did you receive a basic physics treatment of it ( just using the basic equations, v= u + at, v^2 = u^2 + 2as, etc etc) or a mathematical treatment of it, using calculus to derive the equations from knowing the acceleration and substituting in initial conditions? You will need a good knowledge of the second one to incorporate drag.

 

[lukus09]

Okay in response to the personal message, you have no done drag, although you have done projectile motion in a vaccum. Now I'm guessing I am safe in assuming that this was projectile motion in 2 dimensions, but I now need to know, did you receive a basic physics treatment of it ( just using the basic equations, v= u + at, v^2 = u^2 + 2as, etc etc) or a mathematical treatment of it, using calculus to derive the equations from knowing the acceleration and substituting in initial conditions? You will need a good knowledge of the second one to incorporate drag.

i used calculus to derive the equations knowing gravity and initial velocity and angle.
for drag:
I have calculated the horizontal and vertical distances but is there a way where i can combine these two and use theta in the equation to insert the projectile angle?

 

[lukus09]

or how can i find the angle launched from a vertical vs horizontal displacement graph?

 

[Gib Z]

Is that the original problem? You should have said that, that's relatively easy.

Take the lowest set of data points you can see, eg 0.05m x, 0.07y. Draw a triangle, find the angle with trigonometry. The closer your data points are to zero, the closer they will represent the direction of motion before drag and gravity effected the linearity of the motion as much.

 

[lukus09]

no it isnt, i woud like to plot the angle against displacement, how hard is that to do?
do i need to know the object mass and surface area (to work out Cd) to find it?

 

[Gib Z]

Well yes, the resistive force on the object will be proportional v^2, and the constant of proportionality depends on some properties of the object, you can work it out by some simple research online.

Set the new problem up just like you set up your old problems. You started by drawing a free body diagram to find the acceleration in the horizontal and vertical axises, do the same here.

 

[lukus09]

i have produced a graph vertical against horizontal distance. However when the projectile angle is closest to angle of 0 it goes the furthest,what is the problem here. Is the horizontal speed for projectile with drag remain Vcos(theta)?