How Can Theta Be Integrated into the Projectile Motion Equation?

[chillb0y]

Projectile Motion Derivation

Homework Statement

I am supposed to derive an equation that ends up giving me a solution for the initial muzzle velocity of the projectile launcher. I am given different sets of theta and the recorded distance for the x distances. The height of the projectile launcher is also .25m.

Homework Equations

I used dx = Vixt, dy = viyt2 + (1/2)at2 to somewhat isolate the Vix and Viy variables.

The Attempt at a Solution

After isolating the variables, I plugged them into the a2 + b2 = c2 formula (cause the two components form a right angle to find the overall velocity)

i got this equation..

sq((dx2 + (dy-(1/2)at2)2)/t2) = Vi

the thing I am frustrated atm is that I am supposed to integrate theta into the equation but I cannot find a way to do this. it seems like the only varying variable would be dx, but now that i look at it again t should be a varying variable as well? and dy? so now it's more of a mess than an equation.

would love help, this has been giving me a headache for a while.

*edit: if it helps i calculated that a projectile i nthe projectile launcher is in there for only .224s.

 

[chillb0y]

ok after some more analysis i figured out the velocity of the x component all the time (6.84m/s). now having ViX i need to derive a formula so i can use the time from the dy axis and plug it into the dx=vixt

somewhat like this

dy = viyt + .5at2
dx = vixt

Viy = tan theta vix (i am given vix and theta)

 

[chillb0y]

ok i think i got it

solve for Dx

dy = (tan theta vix)(dx/vix) - (g/2)(dx/vix)2

 

[Attique Qasim]

tell me projectile motion equationsin 3d

 

[LawrenceC]

Hints:

1. The velocity in the x direction is constant. So if you know the time of flight, you can determine the distance as a function of the x component of initial velocity.

2. You have two unknowns in the above. They are initial velocity and time.

3. Come up with another equation that will have both unknowns present. To do this, work with the y directon.