Analyzing the kinematic x(t) equation

[brusier]

Homework Statement

Solve the equation below for deltaX symbolically and simplify the answer as much as possible.

deltaY = (tan A)deltaX - g*deltaX^2/2V(initialx)^2

Homework Equations

quadratic equation.

The Attempt at a Solution

I can handle the algebra and simplification. My question comes as I analyze the equation as a kinematics problem. I assume the fnal term was gotten by the equation:

V(final)^2 = V(initial)^2 + 2ax. Therefore V(final) = 0 so there is a deceleration. But g is divided by this accel so I guess g is dependent on this acceleration??

I also found, that given the velocity v time graph, V(initial) = tan A.

Why wasn't this value used in the g*deltaX^2/2 V(initialx)^2 term?

Finally, because I don't see any t in the equation, I assume it can be used in terms of deltaX as well?? Or was the professor just testing our understanding of the quadratic equ?

Does this quation describe any familiar motion?

 

[rl.bhat]

deltaY = (tan A)deltaX - g*deltaX^2/2V(initialx)^2
Dimensionally this equation is not correct. One t is missing.
I also found, that given the velocity v time graph, V(initial) = tan A.
V initial cannot be tanA