Unit 5 Summary: Particle Models in Two Dimensions

In this unit, we applied previously learned concepts to a new model. This model particularly focuses on projectile motion. We used the kinematic equations to calculate the unknowns of different scenarios.

Motion Maps:

The motion maps to the left represent the motion of a ball being thrown forward. The left side represents the ball's motion in the horizontal direction, while the right side represents the ball's motion in the vertical direction. As you can see with the motion maps, the horizontal and vertical motions of a projectile are completely independent of one another. The ball moves with constant velocity in the horizontal direction since there are not any forces acting upon it in the horizontal direction. However, the ball accelerates in the vertical direction downward due to the force of gravity that is acting upon it. The force of gravity is the ONLY force acting upon the ball in this direction.

Formulas and Units to know:

Horizontal:

Δx=vi Δt

vi = vf

Vertical:

vf =gΔt+vi

y = 1/2aΔt2 + viΔt vf2 = vi2+ 2gy y=1⁄2(viy +vy)Δt 

Concept Practice:

1. 

A ball is thrown downward with an initial speed of 15 m/s.
What is the acceleration of the ball? Calculate the displacement of the ball during the first 3 seconds.

Now calculate the time required to reach a speed of 40 m/s. Also, calculate the speed of the ball after falling 80 meters.

2. John's dog is chasing a cat across a table surface 1.3 m high. The cat quickly jumps off the table as John's dog slides off of the table at a speed of 4.2 m/s. Where will John's dog land on the floor?

3. A baseball is thrown straight upward and return to the thrower's hand after 4 seconds in the air. A second ball is thrown at an angle of 40 degrees with the horizontal. At what speed must the second ball be thrown so it reaches the same height as the one thrown vertically?

4. A group of students are visiting the Empire State Building while on a trip to New York City. A student becomes quite angry at another student and decides to throw him off from the observation deck, which is 371 meters high, with an initial downward speed of 10 m/s (pretend that the steel barriers that surround the observation aren't there). How long does it take the student to hit the street below? How fast is the student going at the moment of impact?

5. An angry student hurls an apple out of a window with a velocity of 14 m/s at an angle of 25 degrees above the horizontal. If the launch point is 8 meters above the ground, how far from the building will the apple hit?

Conclusion:

In this unit, I learned about projectile motion. I used previously learned concepts and applied it to models in two dimensions. I learned that the kinematic equations that apply to the the vertical component have to be associated with CAPM and UFPM. The formulas that apply to the horizontal have to be associated with BFPM and CVPM. At the beginning of the unit, I discovered that motions that occur on the horizontal and motions that occur on the vertical are completely independent of each other. I further used trigonometry to calculate the Viy and the Vix, which we applied to the latest challenge in class, the rocket challenge.  

Sources Cited:

http://paynephysics.wikispaces.com/file/view/Particle+Models+in+Two+Dimensions.pdf

http://w3.shorecrest.org/~Lisa_Peck/Physics/All_Projects/photojournal/shelby/shelby.html