Where does this kinematics equation come from?

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The equation g(t)/vox=tan(theta) represents the relationship between the vertical and horizontal components of a projectile's motion. Here, g is the acceleration due to gravity, t is time, and vox is the initial horizontal velocity. The discussion clarifies that this formula derives from the basic trigonometric identity tan(θ) = Vy/Vx, where Vy is the vertical velocity influenced by gravity over time. The participants explain how the equation can be used to determine the angle of a projectile's trajectory after a certain time. Understanding this relationship helps in solving projectile motion problems effectively.
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g(t)/vox=tan(theta)

g= acceleration due to gravity (9.8m/s^2)
t= time
vox = initial velocity in the x direction

Where does this equation come from?? someone told me to use this to help me solve one of my homework problems and it worked but i have never seen it before and am having a hard time to figure out where the components of the equation actually come from?

could anyone help explain this equation to me?

thank you
 
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mybrohshi5 said:
g(t)/vox=tan(theta)

g= acceleration due to gravity (9.8m/s^2)
t= time
vox = initial velocity in the x direction
This looks like a formula for calculating the angle below the horizontal that a projectile will be moving after time t after being released with a purely horizontal speed of V0x. It's just tanθ = Vy/Vx. Vy = at = gt.
 
Hi mybrohshi5! :smile:

(have a theta: θ and try using the X2 tag just above the Reply box :wink:)

If at time t, the angle is θ and the speed is v, then

vsinθ = gt

vcosθ = vx0,

so tanθ = gt/vx0 :wink:
 
thank you both! that makes complete sense now.
 

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