• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Scoring a Basket.

Extracts from this document...

Introduction

MATHS COURSEWORK – SCORING A BASKET

Task: Find values for the initial speed and angle of projection needed to score a basket in basketball from the free throw line. Is there a range of values of angle for an initial velocity that will still allow you to score a basket?

Method: To solve this problem I am going to record myself scoring 10 clean baskets (the ball does not touch the hoop or back board) on video camera. Having done this I will know the time taken from the ball leaving my hands to it going into the basket. By using vector equations for Displacement, Velocity and Aceeleration in relation to time I will be able to calculate:

  • The maximum height achieved by the ball.
  • The distance travelled by the ball
  • The time taken to travel this distance
  • The height of release and the height at which it lands.

This will give me an accurate model of the balls motion through the air. I will be able to use the velocity vector equations to find the horizontal and vertical components of velocity for each throw. Using Pythagoras Theorem I will be able to calculate the initial velocity. Using trigonometry I will also be able to calculate the angle of release. This will allow me to analyse how initial velocity and the angle of release are related and therefore allow me to find a range of values for the angles of release for a given velocity.

...read more.

Middle

3

1.03

1.950

54.339

7.614

4

1.01

1.903

53.468

7.605

5

1.1

2.125

57.232

7.679

6

1.07

2.049

56.021

7.645

7

1.16

2.286

59.521

7.770

8

1.12

2.178

58.014

7.706

9

1.06

2.024

55.608

7.636

10

1.09

2.099

56.833

7.667

Average

1.077

2.070

56.252

7.663

I have also investigated the velocity needed to achieve a basket for any given angle. Although I dont know the values for the horizontal and vertical components of velocity they can be represented by

[             ]

These values can be put into the position vector equation to give:

[                            ]

I know that the horizontal component is equal to 4.572 m so I can rearrange to give:

This can then be substituted into the vertical component of the position equation. This leaves only t as an unknown quantity so:

This gives the total time for the throw. This value can now be substituted into the velocity vector equation to find the initial velocity as shown earlier.

...read more.

Conclusion

        Finally, the experiment in general had the possibility for a lot of errors. For example there was human error involved in the timing of each throw and the measuring of the release point so the answers derived from these values would be inaccurate. Also because there are so many calculations it means that any error gets increasing multiplied to cause an even bigger inaccuracy. Having said this there isn’t a lot that can be done to gain more accurate results without using advanced equipment. For example light gates could be used to measure the time of the throw more accurately and machines could be used to throw the ball so that the release height, velocity and angle could all be better controlled.  

There are a number of things that could be investigated to achieve a more accurate representation of the angles needed to score a basket. Firstly I only looked at the angle of release for one release height. If the release height was higher or lower then the release angle could change or the velocity needed for a certain angle would be different which might make the optimum angle for different people. Secondly you could look at the affect of jump shots from the free throw line, again this is increasing the release height.  

...read more.

This student written piece of work is one of many that can be found in our GCSE Forces and Motion 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 GCSE Forces and Motion essays

  1. Bouncing Ball Experiment

    Table showing Variation between Results Height the ball bounced to (cm) (h2) Height the ball was dropped from (cm) (h1) repeat 1 repeat 2 repeat 3 repeat 4 repeat 5 Variation Between Results(cm) 200 105 103 109 104 106 6 190 104 103 104 102 103 2 180 102 102

  2. This investigation is associated with the bounce of a squash ball. I will be ...

    So if the average width of the test strip is exactly 15mm, the minimum force required to break the seam must be 90 Newtons. Rebound resilience is simply a measurement of the height a ball bounces off a hard surface.

  1. Squash Ball and Temperature Investigation

    Repeat the entire experiment again (i.e. heating the ball at 300C and then dropping it) for heights 40cm, 50cm, 60cm etc going up in 10 cm's till you reach the height of 1 metre. 5. Arrange the collected data from the experiments in a table so that they can

  2. Investigation into the range of a ski jump

    A straight line graph is needed to give a conclusive correlation, in the form: y=mx+c Where: y is the position on the y axis x is the position on the x axis m is the gradient c is the point of y intercept Therefore the formula must be rearranged in the straight line graph form.

  1. Investigating the amazingness of theBouncing Ball!

    As you can see from the graph overleaf, the highest range between any two points at a certain bounce is 0.02. This shows that my results are almost completely accurate and that the Dr Daq system will be very useful in obtaining results for this investigation.

  2. Gaydon Technology Partnership Centre

    required to withstand a force of 20g for a speed of 30m/s but to increase safety standards for their drivers landrover test to a standard of 30g for a speed of 30m/s.The crash sled consists of a seat or the component being tested on a rails connected to 10 bungy

  1. How does height influence velocity.

    Here is an example of how to calculate 2GH: If the height was 5 cm the equation is: 2 x 9.8(the gravitational pull) x 0.05m= 0.98 m/s Friction is the force that slows down moving objects. The size of the friction force depends on the roughness of the surfaces: the rougher the surfaces, the greater the friction force.

  2. Motion of an object as it slides down a slope at different angles to ...

    The measurement is made from the floor perpendicular to the table edge to the nearest mark that is parallel to the edge of the table. This is because I have chosen to measure l from the bottom of the cylinder - measuring where it cuts the paper will be equivalent

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