PARABOLIC TRAJECTORY

PARABOLIC MOTION

AMOUNT

Chapter one, Preface

1.1    hypothesis

1.2   purpose of the observation

1.3  background

1.4  form of the problem

Chapter two, Review theory

Chapter three, Methods of research

3.1 place and time

3.2 materials

3.3 methods

Chapter four, Research Result

4.1 Result

4.2 Data analysis

Chapter five, Discussion and Conclusion

5.1 conclusions

5.2 suggestions

Bibliography

Physic

Parabolic trajectory

Chapter one

Preface

1.1     background

Physic has close relationship with our daily life; everything we do can be is can be explain by physic. For example: basket ball game is one of favorite sport around the world, so many people love that game. To play this sport game, we must shut ball to ring, which is characteristic of this game, team who enter ball more will win. We know the rule to play basket ball but maybe we don’t know about physic concept contain in basket ball. When we throw up the ball to ring, the ball will slide to ring with unique trajectory, we can observe: at the first we throw, the ball will move vertically and then when the ball reach particular height it will move downward. We also can analyze what happen with the ball when it thrown. We also can observe the initial velocity, velocity in highest point and final velocity.

Especially in this work paper we analyze about basket ball motion with physic equation. Physic concept will be use is about parabolic motion, and initial velocity.

1.2    form of the problem

What is influence about distance of basketball player toward basketball ball velocity in parabolic motion?

1.3    purpose of the observation

·         To find out effect of physic concept in daily life especially in

·         We will know about parabolic motion in basket ball game

·         To find out that initial velocity in parabolic motion is depend on distance and gravitation

1.4   hypothesis

When player throw up ball from particular distance we can also know the initial velocity of the ball depend on it distance, ring height, player height and gravitation

if we stand near the ring we will get low initial velocity, and if we throw the ball far from the ring we will get high initial velocity

Chapter two

Review theory

A trajectory is the path that a moving object follows through space as a function of time. The object might be a projectile or a satellite, for example. It thus includes the meaning of orbit—the path of a planet, an asteroid or a comet as it travels around a central mass. A trajectory can be described mathematically either by the geometry of the path, or as the position of the object over time.
In control theory a trajectory is a time-ordered set of states of a dynamical system (see e.g. Poincaré map). In discrete mathematics, a trajectory is a sequence of values calculated by the iterated application of a mapping f to an element x of its source.

Basket ball is an object upon which the only force is gravity. Gravity, being a downward force, causes a ball to accelerate in the downward direction. The force of gravity could never alter the horizontal velocity of an object since perpendicular components of motion are independent of each other. A vertical force does not effect a horizontal motion. The result of a vertical force acting upon a horizontally moving object is to cause the object to deviate from its otherwise linear path

According to Newton's law of inertia, an object in motion in a horizontal direction would continue in its horizontal motion with the same horizontal speed and direction unless acted upon by an unbalanced horizontal force. The animation above shows a green sphere moving to the right at constant speed. The horizontal distance traveled in each second is a constant value. The red sphere undergoes a vertically accelerated motion which is typical of an object upon which only the force of gravity acts. If these two motions are combined - vertical free fall motion and constant horizontal motion - then the trajectory will be that of a parabola. An object which begins with an initial horizontal velocity and is acted upon only by the force of gravity will follow the path of the blue sphere. It will travel the same horizontal distance in each consecutive second but will fall vertically a greater distance in each consecutive second.

A trajectory is the path that a moving object follows through space as a function of time. The object might be a projectile or a satellite, for example. It thus includes the meaning of orbit—the path of a planet, an asteroid or a comet as it travels around a central mass. A trajectory can be described mathematically either by the geometry of the path, or as the position of the object over time.
In control theory a trajectory is a time-ordered set of states of a dynamical system (see e.g. Poincaré map). In discrete mathematics, a trajectory is a sequence of values calculated by the iterated application of a mapping f to an element x of its source.

Chapter three

Methods of research

3.1 place and time

Place: SMA 2 KEDIRI’s basketball field

Time: Tuesday, 27 September 2011 (at physic period 07.00-08.00 )

3.2 materials:

·         ruler

·         basket ball

·         ring

·         field

·         marker

3.3 methods

·         measure high of the ring

·         measure high of the player

·         measure distance between basket ball player and the ring about:

550cm,500 cm,  450cm, 400cm, 380 cm, 350 cm

·         mark it with marker

·         throw the  ball to ring

·       

4.1 Result

Known: height of ring: 305 cm  

Player height: 156 cm

            So Y axis: 305 – 156 = 149 cm

X axis= 

 a. 300 cm      d. 450 cm

b. 380 cm        e. 500 cm

c. 400 cm       f. 550 cm

We use tangent and x axis formula

tanθ = y/x

            X = V02 . sin α . cos α

                                  g

                              

       

TABLE OF DATA

Distance (X axis)(cm)	Height (Y axis)(cm)	Angle	Initial velocity (cm/s)
300	149	= 23.06⁰	98.766
380	149	21.41⁰	106,084
400	149	20.45 ⁰	110.6o
450	149	18.32⁰	122.88
500	149	16.59⁰	135.162
500	149	15,158 ⁰	147.622

 

4.2 Date analysis

From data above we can conclude distance of ring is effect initial velocity and also effect angle of elevation. Based on tangential rule and velocity formula,  If X axis is show small value the velocity value is also small and it angle value is more big.

           

Chapter five

5.1 conclusions

From basket ball experiment we know that distance(X) influence to initial velocity of the ball, another factor who effect the initial velocity in parabolic motion is gravitation, angle, player height and ring height (Y).

if the distance is near we will get low initial velocity and if the distance far from ring we will get high value, this statement mean hypothesis is proven

5.2 suggestions

The suggestion that give is: to know the parabolic motion component we can do this experiment again and the result can compare with this working paper. So the result of this experiment is more accurate. Except  that we can do and try another experiment about parabolic motion, for example parabolic motion in football game, parabolic motion in bungee jumping etc . We will more understand about physic concept especially in parabolic motion in our daily life.

Bibliography:

http://www.footbag.org/reference/-/Parabolic_motion

http://wikipedia/trajectory project/Trajectory

http://www.bds.trajectory project/bds.cfm

Ogif ratunar R/22/XI IA 3