PHYSICS BASEBALL TRAJECTORY

                                                    Baseball Trajectory

A parabola represents the trajectory of many round objects when thrown from rest.


The Problem:  Find the Trajectory of the baseball when thrown.

The Formula:  (The Polar Equation) 1/r=a cos(A+B) + k/h^2

**T is representive of time**
**r is radial distance from origin at time T**

We can do this problem similar to the pendulum problem...(Use the quadrant plain as a backdrop, start at orgin and imagine throwing a baseball.

The ball will accelerate once the force is given (Bigger biceps = Greater Force........Just sayin)..


Once the ball leaves the origin of the quadrant plain it will begin to slow down or (decelerate) due to the opposing forces, and at the
heighest point.

The ball will have no acceleration/deceleration due to the forces cancelling each other out, to a certain extent..........

You can imagine the ball(Once reaching highest point on the plain) starting to slow down until nothing...THEN....The Ball picks up speed

again due to gravity.


We have considered the scenario on the quadrant plane.....NOTICE: At the highest point where you picked your plot on graph a horizontal line can be

placed on top of the point, showing that no acceleration is taking place.  Once it starts picking up speed and going in the forward x direction (due

to the dimensionality of space and time) one can place a downward sloping line (showing it is accelerating....Remember it's all about direction when

considering acceleration/deceleration....(That's why we define our position before beginning....)


This is just a reminder of what the calculus is telling us....Remember the definition of a derivitive(change in place over time).

Now.....

if we place the situation in the dimensions physics has brought to our attention:

Acceleration due to gravity = (-9.81 m/s^2)

Our origin in space and time is our hand at rest, in regards to the quadrant plain; this could be in any of the quadrants....


NOW ON TO THE PROBLEM....

A=Angle the ball makes from x-axis

t=seconds

r=radial distance of ball from origin at time (t)

R=Radius of Mass the ball is curving into.  Example:  Earth, Jupiter, Mars.... If put in latter environments, the acceleration due to gravity will
change drastically due to the mass of the planet.

g=gravitational pull of mass curving ball...On earth = -9.81 m/s^2.....

k=(k is constant that is derived from Newtons Law...k=gR^2

h= r^2 (dA/dt)....h is constant of angular momentum

a= a is a constant in front of cos

B= constant angle on plain...-pi/2 <= B <= pi/2...essentially saying we are restricted in this domain....

(Remember your Trigonometry on this part)!!!


**********Eazy Peazy***********

I will be back with solution at later date...

..........CHECK IT OUT........VISUALIZE IT.......LEARN IT......SOLVE IT.....