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

 

[nlightner]

I would approach this problem by first identifying the variables and their units. In this case, we have deltaY (m), deltaX (m), tan A (dimensionless), g (m/s^2), and V(initialx) (m/s). The equation can then be rearranged to solve for deltaX, which is the change in position in the x-direction.

In terms of kinematics, this equation can be interpreted as the displacement in the y-direction (deltaY) being dependent on the displacement in the x-direction (deltaX), as well as the initial velocity (V(initialx)) and the angle of the trajectory (A). The term involving g is the acceleration due to gravity, which is dependent on the initial velocity and the angle of the trajectory.

The use of the quadratic equation is appropriate here, as the equation describes a projectile motion with a deceleration due to gravity. The value of V(initialx) is not used in the g*deltaX^2/2 V(initialx)^2 term because it is already incorporated in the term tan A, which represents the initial velocity in the x-direction.

Since there is no time variable in this equation, it cannot be used to describe any specific motion. However, it can be used to calculate the displacement in the y-direction for any given displacement in the x-direction and initial conditions.