• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month
Page
  1. 1
    1
  2. 2
    2
  3. 3
    3
  4. 4
    4
  5. 5
    5
  6. 6
    6
  7. 7
    7
  8. 8
    8
  9. 9
    9
  10. 10
    10
  11. 11
    11
  12. 12
    12
  13. 13
    13
  14. 14
    14
  15. 15
    15
  16. 16
    16
  17. 17
    17
  18. 18
    18
  19. 19
    19
  20. 20
    20
  21. 21
    21
  22. 22
    22
  23. 23
    23
  24. 24
    24

Modeling a basketball shoot in the lab

Extracts from this document...

Introduction

Modelling and investigating the farthest range from which a basketball can be shot into a ring

image00.jpg

By Janice Lau (U6th)


Content Page

Aim

Background Information

Calculations and Diagram- prove that it’s a parabola

Theory- PROJECTILE MOTION AT AN ANGLE

How to model a basketball shot?

Apparatus

Force vs. Compression – Spring Loaded Plunger

Prediction/Safety

Experiment 1 - Preliminary investigation

Experiment 2

Research about Basketball

Experiment 3

Experiment 4

Experiment 5

Conclusion

Evaluation

Source

3

3

4

5

6

6

6-10

10

11-12

13-14

15

15-17

17-18

19-20

20-21

21

21


The AIM of my investigation is to find the optimum angle for the maximum range for a basketball shot by modeling it in the lab.

Background- PROJECTILE MOTION

Definition: “An object launched into space without motive power of its own is called a projectile. If we neglect air resistance, the only force acting on a projectile is its weight, which causes its path to deviate from a straight line.”1

The projectile has a constant horizontal and vertical velocity that changes uniformly when it is influence by acceleration and gravity.

Diagram:

Fig 1 &2 shows that basketball shots are projectile motions, however, how can we show it mathematically?

Calculations

Consider the horizontal and vertical motion individually. Initially,

Ux = u cos θ ----- (1)

Uy = u sin θ----- (2)

The horizontal velocity is constant through out the motion, since the acceleration is vertically downwards. At time t, the velocity components are

Vx = Ux = u cos θ ----- (3)

Vy = Uy – gt = u sin θ –gt ----- (4)

The horizontal and vertical displacements of the objects are:

X= Uxt = ut cosθ ----- (5)

Y= Uy – ½ gt2 = ut sin θ – ½ gt2 ----- (6)

From equation (5) we have,

t= x/ u cos θ

Putting t into equation (6), the equation of trajectory is,

y= x tan θ – g/2u2 cos2 θ

...read more.

Middle

Precautions/ Safety:

Before the experiment, I handed in a plan and was approved at a safety angle by teacher. During the experiment I have also considered many aspects of safety issues. For example, making sure that when I shoot the ball with the spring loaded plunger, I would not hit anyone and the use of balls; making sure the ball is not hard to hurt anyone.

Error in Range and % error calculation

Error in range = (max range – minimum range)/2

% error calculation = Error in range / Average Range

The following graphs’ error bars are plotted using the average percentage error.


Preliminary Investigations

In this investigation, a table tennis ball is chosen for trials because it is very light and is able to be fired off to a long distance.

Method:

I shoot a table tennis ball towards a sand pit at different angles using a “small” force and measure the range of the ball when it first land using a tape measure. I then record the corresponding horizontal distance as the angle varies; where angle is measure using a protractor. (Apparatus set up based on Fig 3.- without light gate)

Prediction:

I expect that the optimum angle for maximum range will be around 40-50 degrees, according to the theoretical value 45 degrees I have calculated earlier.

Results:

Diameter of the table tennis ball: 29 mm         Average weight of the ball: 2.6 g

Angle

(Degree)

Range/ Horizontal Distance (m)

1

2

3

4

5

Average

Error in range

% Error in range

20

1.10

1.15

1.10

1.12

1.08

1.11

0.03

3

25

1.15

1.10

1.18

1.12

1.12

1.13

0.04

3

30

1.17

1.13

1.15

1.14

1.16

1.15

0.02

2

35

1.13

1.14

1.20

1.20

1.09

1.15

0.05

5

40

1.03

1.06

1.07

1.01

1.14

1.06

0.06

6

45

1.05

1.10

0.94

0.99

1.07

1.03

0.08

8

Table2. Shooting a table tennis ball with a ‘small force’- (for experiment 1)

Average error in range= 0.05 = 5%

image16.png

Graph 2: Angles vs. Horizontal Distance- (for experiment 1)

...read more.

Conclusion

5

41±5

"Big" force + squash ball+ sand pit at the same level as the shooting point

Conclusion

As the height of sand pit increases to level with launch, with a constant shooting point, the optimum angle increases and will be closer to the theoretical angle of 45 degree as it get to the same level as the shooting point.
From the results above, I can predict and expect that when the height of the sand pit is fixed (a basketball ring- in real life), the optimum angle for a lower shooting point (short person) will be further from the optimum angle than from a higher shooting point (a taller person).

Evaluation

Although my experiments proved the trend between height and optimum angles, there are lots of other ways to further investigate and improve my investigation.

There are errors in measurements

  • Apparatus error e.g. the accuracy of protractor and ruler for measurements is ±0.5 cm and ±0.5 degree respectively.
  • Inconsistency of the force when shooting using a spring loaded plunger

To improve my investigation, I can firstly use more accurate apparatus. Then have a better and wider range of results with a smaller interval between results.

For further investigations, I then find out the relationship between different types of balls and different speed of balls and see how they affect the optimum angle of a shot.

Sources

  1. http://apcentral.collegeboard.com/apc/members/repository/ap03_projectile_motio_30832.pdf (reference for definition)- page1
  2. http://www.lightingsciences.ca/pdf/BNEWSEM2.PDF
  3. Advanced Physics (p.118) by Tom Duncan
  4. Mechanics 2 by John Hebborn and Jean Littlewood
  5. http://galileoandeinstein.physics.virginia.edu/more_stuff/Applets/ProjectileMotion/jarapplet.html
  6. http://apcentral.collegeboard.com/apc/members/courses/teachers_corner/30827.html
  7. facstaff.gpc.edu/~ulahaise/The%20Physics%20of%20Basketball.ppt
  8. http://apcentral.collegeboard.com/apc/members/repository/ap03_projectile_motio_30832.pdf

...read more.

This student written piece of work is one of many that can be found in our AS and A Level Fields & Forces section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related AS and A Level Fields & Forces essays

  1. Marked by a teacher

    Experiment to determine gravity from a spring using digital techniques

    3 star(s)

    The gradient is . The uncertainty in g is calculated by combining this uncertainty value with the uncertainty for k. So the value for g calculated in this experiment is: Uncertainty in Each Point The uncertainties in the mass are once again �0.001kg, which is very small, and again the error bars on this graph are too small to see.

  2. Peer reviewed

    Determination of the acceleration due to gravity (g)

    4 star(s)

    reading an instrument incorrectly or recording the wrong number. Errors may also occur because of the limit of precision of equipment involved. There are two variables measured in the experiment, they are height and time. So all the errors in the finding out g come from the error of measuring of height and time.

  1. The experiment involves the determination, of the effective mass of a spring (ms) and ...

    The readings are shown in the order that they were taken. They were taken in this order, to check that the masses, which were to be used were usable. i.e. the smaller masses did not oscillate to quickly to be measured and that the larger masses did not damage the spring.

  2. Experiment to determine gravity from a spring using analogue techniques

    uses the period squared, and the total uncertainty for each period squared value can be calculated. A sample uncertainty calculation is shown below. Mass = 0.01kg Random = �0.05s Reading = �0.05s Calibration = 2% x 2.9 = �0.058 As a percentage of 2.9, this is 1.1%.

  1. Objective To find the acceleration due to gravity by means of a simple ...

    Timing stops at the beginning of the third interruption, as the pendulum complete one full oscillation.

  2. Stopping distance Investigation.

    PREDICTION AND SCIENTIFIC BACKGROUND: For this investigation, I predict that as the mass of the vehicle increases, so will the stopping distances of it. This is because the trolley will become heavier, and so stronger forces will be needed to bring it to a halt.

  1. Investigating the relationship of projectile range and projectile motion using a ski jump.

    Vx = V cos ? Vy = V sin ? The projectile/ball baring will be dropped from the top of the ramp giving the projectile gravitational potential energy. We can work out the gravitational potential energy by using ?Egrav = mg?h as we know the mass of the projectile, gravitational effect and the height at which the projectile is launched.

  2. Experiment to calculate spring constant of 2 springs

    Spring 2 As shown before: Calculating the Uncertainty in "k" In order to calculate the uncertainty for each value for k, the LINEST function in excel was used. Spring 1 Spring 2 Part 2 Mass 1 = 0.273112kg Time (s)

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work