Thursday, March 3, 2016

Projectile Motion Summary


Over the course of the unit, I have collected meta notes on each worksheet or activity that we did.
·      I learned that when you solve for the time, plug in Vix for initial velocity.
·      Always plug the acceleration or displacement in as a negative number.
·      When a problem does not give you the Vi in the horizontal or vertical direction, split the velocity into components and use cosign to solve for the Viy and Vix.
·      Remember:
o   How long/ how far: displacement (change in X)
o   How fst: velocity
·      The only formula that can be used in the horizontal direction is:
Vx= Change in Xx
              T

Rules:
1.     If an object starts at rest or is dropped then the Vi is 0.
2.     When something is falling down in the vertical direction, the acceleration and displacement is negative.
3.     The only force acting on an object falling is gravity, therefore the acceleration is negative because gravity is going downward.
4.     Whenever an object is at it’s highest point, before it turns around and accelerates downward, the velocity is 0 at the highest point.
5.     The only formula that can be used in the horizontal is Vxx equals change in Xx over change in time.
6.     When an object is thrown up and the returns to the ground vertically, the displacement is always 0.
7.     If the path of an object in moving upward, the displacement is positive
8.     If the path of an object is moving downwards, the displacement is negative
9.     Always use cosign to solve for the components of Vix and Viy
10. When using the quadratic formula, always use the positive answer for time.

Formulas:
o   x= 1/2at^2+viy(t)
o   vf=at+ vi
o   vf^2=vi^2+2(acceleration)(change in x)
o   a= change in v/ change in t

Key:
Here are the models the apply to the vertical or horizontal sides. When doing a goalless problem, here are all the variable to solve for:

Vertical:
o   -Unbalanced forces
o   CAPM
o   UFPM
o   Acceleration
o   vf=at+ vi
o   x= 1/2at^2+viy(t)
o   vf^2=vi^2+2(acceleration)(change in x)

Horizontal:
o   BFPM
o   CVPM
o   Constant velocity
o   Vx= Change in Xx
            T



Example:

NASA launches a rocket horizontally with a 7.0 m/s off a crater on the moon. How far will it travel horizontally before it strikes the ground outside the crater 15m below? (Disregard the lack of gravity outside of earth).

First, write all the horizontal and vertical knowns and unknown. As we solve for each variable we will go back and plug in what we found.

Horizontal:
o   Vi= 7m/s
o    Displacement= ?
o   t= ?
o   a= -10m/s
Vertical:
o   displacement= 15m
o   a= -10m/s
o   Vi= 0
o   T=?

First, use the following formula to solve for the time.

Change in X= 1/2at^2+Vit
-15= ½(-10)t^2+0t
-15=-5t^2
  - 3         -3

t= 1.73s

Now plug in the time into the horizontal equation to find the displacement.

Velocity= change in X
                    Time

7= X    
      1.73
displacement= 12.11m


Now plug in the variable solved for into the horizontal and vertical lists.
Horizontal:
o   Vi= 7m/s
o    Displacement= 12.11m
o   t= 1.73s
o   a= -10m/s
Vertical:
o   displacement= 15m
o   a= -10m/s
o   Vi= 0
o   T= 1.73s

Describe the motion of the rocket in the x-direction and explain why it moves in that manner.

The rocket moves in the x directions with no acceleration and the only force acting on it is gravity. Gravity only affects the vertical direction.

Describe the motion of the rocket in the y-direction and explain why it moves in that manner.
It drops 15m and moves downwards with acceleration of 10m/s, with only the force of gravity acting on it. There is an unbalanced force of gravity, which causes it to speed up.

The picture above is a projectile motion map, showing the projectile motion of a ball being thrown. The ball is thrown upward in its path, reaches the top, and then changes direction and accelerates downward.

Projectile Motion in Real Life:
Projectile motion can be applied in engineering designs. In oorder to design machinery, you have to have a concept of gravitational acceleration and the ability to predict the path of motion usuing mathematical formulas. By being able predict the trajectory of objects, can help students complete labs more efficiently. At the conclusions of this unit, students had many assets under their toolbelts to solve labs. We could use Pasco capstone, different kinematics formulas to solve for a specific variable, or use a force diagram and scale to solve for different forces.
 

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