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Transcript of Projectile Motion
We need to know the formula needed to calculate the path of a projectile.
What is a projectile?
How do we find the path of projectiles?
A projectile is defined as any object moving through the air or space, with only gravity acting upon it.
In order to figure out the path of prjectiles, one needs to understand that all projectile motion is, is a combination of horizontal and vertical motion. One of the most important things to remember is the fact that the downward motion of a projectile is the same as a free falling object.
So what am I really doing?
this final project is supposed to give the students a review of projectiles, while moving into more "mathy" bits when dealing with a projectile launched at and angle.
The math behind the madness
Inorder to find out exactly where a projectile will land, one must find out a few componets.
we need to find the starting values of at least two of the variables.
we need to put it all together
As we had previously learned, the equation for projectile motion is
However, in this particular case, I am going to use two different equations to find the same solution.
I am doing this because we now have an angle at which the projectile is launched.
These equations are:
I am using these equations because:
Projectile Motion is a combination of horizontal and vertical motion. One of the equations takes care of the horizontal portion, solving for x, and the other one takes care of the vertical componets, solving for y. I changed gravity to be 16ft/sec because for these problems, it is easier to work with.
I am now going to show how these eqations can be used to find where a small ball will pass through a small ring.
We first need to find the initial height of the object, and the horizontal distance it would travel if it were just launched horizontally, meaning the angle would be 0.
In this case, the initial height would be 4.8021, and the horizontal distance would be 9.2257 feet. I got these numbers by simply mesuring them.
After we figure those out, we move on to the initial velocity. To calculate this, we first need to find out how long the ball is in the air when it is launched at 0 degrees. We substitute 0 degrees in for Theta and then simplify the equations above. We end up with:
The substitute the vertical position of the ball when it hits the ground (0) and subsitute that in for the y variable, and solve for t:
by the way, the angle we are working with is 45 degrees!
t becomes .5478 seconds.
Now that we have t figured out, substitue it in the "x" equation and solve for
Initial velocity is 16.8401 ft/sec
Although there is a way to find the horizontal distance the ball will travel algebraically, I personally just put my equations into the calculator and drew a graph. I then traced the graph to find out the distance the ball will travel. In order to find out where the ball will go through the hoop, I needed to find out where the graphs height was as tall as the the ring stand. The overall distance the ball will travel is:
The distance the ring needs to be at is:
When I took all of these values, I was using a table at home that had a different initial height. The fact that we are in a different room, with maybe more air resitance can contribute to the ball not making it through the ring.