# Determine the relationship between the range of the jump achieved by the ski jumper and the dropping height on the ramp.

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Introduction

A-Level Physics Practical Investigation

Walid Aboudi

Ski Jumping

Introduction:

As we all know ski jumping is a worldwide sport in which athletes skate down a slope ramp, gaining speed that throws them in the air that makes them land some distance away. The distance travelled at the time when the jumper leaves the ramp, until he reaches the ground is known as the jump range.

This interesting and challenging sport has a lot of physics behind it. Kinetic energy, gravitational force, motion, speed, height, time, distance and the athlete’s ability to reduce air resistance to his or her body (aerodynamic) are all factors that determine the athlete’s performance.

This experiment represents a ski jumping slope through which we will investigate how physics is related to it.

Aim:

The aim of my investigation is to determine the relationship between the range of the jump achieved by the ski jumper and the dropping height on the ramp. We will model the jumper as a ball and the ski slope as a bent plastic ramp.

Currently at this level we will not take air resistance, friction and other various type of energy lost into account. However in practical we have to take in mind that they do exist and cause variation in our results.

Background knowledge and Predictions:

I have decided to investigate how the vertical height of drop on the slope relates to the range achieved. One of the things a person can think of firstly is that the greater the height on the ramp, the greater the range will be. This is because more GPE is converted into KE.

GPE stands for “Gravitational Potential Energy” and it is the energy that an object has at a certain height. The equation for it is:

“GPE = mgh”, where “m

Middle

There were some errors in my experiment which had to be solved; one of the main errors is the ruler. I used a 30 cm ruler to measure the distance travelled by the ball on sand but I found that the edge of the ruler didn’t start from 0 cm, but 0.5 cm. This kind of error was solved by subtracting 0.5 cm from all the results.

The other kind of error, which I encountered in my experiment, is dropping the ball. When I use to hold the ball in a certain position up the ramp, sometimes it used to give me some strange measurements on the sand tray; I discovered that these uncertainties were caused by a push which is applied by my hand. This problem was solved by using a ruler to hold the ball in position, then by removing the ruler from its place the ball will roll down without any other force has been applied to it.

## Height of slope (m) | ## Actual Range -1-(m) | ## Actual Range -2-## (m) | ## Actual Range -3-## (m) | ## Average Range (m) | ## Velocity(m/s) | ## Time of flight## (s) | ## Predicted## Range (m)(without RKE) | ## Predicted## Range (m)## (With RKE) |

0.062 | 0.196 | 0.197 | 0.198 | 0.197 | 1.102 | 0.280 | 0.309 | 0.261 |

0.133 | 0.243 | 0.234 | 0.238 | 0.238 | 1.615 | 0.280 | 0.453 | 0.382 |

0.197 | 0.276 | 0.275 | 0.267 | 0.273 | 1.965 | 0.280 | 0.550 | 0.466 |

0.281 | 0.320 | 0.317 | 0.316 | 0.318 | 2.347 | 0.280 | 0.658 | 0.556 |

0.364 | 0.374 | 0.334 | 0.343 | 0.350 | 2.671 | 0.280 | 0.749 | 0.617 |

0.456 | 0.387 | 0.361 | 0.361 | 0.369 | 2.989 | 0.280 | 0.838 | 0.708 |

0.558 | 0.408 | 0.387 | 0.384 | 0.393 | 3.300 | 0.280 | 0.927 | 0.783 |

0.695 | 0.426 | 0.418 | 0.419 | 0.421 | 3.690 | 0.280 | 1.035 | 0.874 |

Results:

Angle 34º

Angle 20º

## Height of slope (m) | ## Actual Range -1-(m) | ## Actual Range -2-## (m) | ## Actual Range -3-## (m) | ## AverageRange (m) | ## Velocity(m/s) | ## Time of flight## (s) | ## Predicted## Range (m)(without RKE) | ## Predicted## Range (m)## (With RKE) |

0.031 | 0.164 | 0.165 | 0.166 | 0.165 | 0.779 | 0.280 | 0.219 | 0.185 |

0.069 | 0.205 | 0.206 | 0.203 | 0.205 | 1.163 | 0.280 | 0.326 | 0.275 |

0.109 | 0.249 | 0.245 | 0.237 | 0.244 | 1.462 | 0.280 | 0.410 | 0.346 |

0.149 | 0.292 | 0.297 | 0.291 | 0.293 | 1.709 | 0.280 | 0.479 | 0.405 |

0.195 | 0.328 | 0.325 | 0.332 | 0.328 | 1.955 | 0.280 | 0.548 | 0.463 |

0.241 | 0.345 | 0.341 | 0.351 | 0.346 | 2.173 | 0.280 | 0.609 | 0.515 |

0.295 | 0.380 | 0.382 | 0.385 | 0.382 | 2.405 | 0.280 | 0.674 | 0.569 |

0.36 | 0.415 | 0.412 | 0.408 | 0.412 | 2.656 | 0.280 | 0.745 | 0.629 |

Conclusion

Evaluation:

The experiment generally went according to plans with no significant problems to speak of. The results I obtained were very satisfying except for angle 34º which appeared to produce some bizarre results because I dropped the ball with my hand, which must have given it a push. But that did not affect the general outcome as the results obtained from dropping the ball when the ramp was at angles 15° and 20° which gave perfect results.

Because it is a practical investigation, then equations have to be derived from the experiment results. And in order to make sure that these equations make sense, they must be compared to other theoretical equations which are used for comparison reasons only.

The equation obtained from the experiment matched the theoretical equation when the slope was at 20° by up to 96.5%. If we take into consideration human error, friction and air resistance, this result can be considered a perfect one.

My aim in this investigation was to determine the relationship between the range of the jump achieved by the ski jumper and the dropping height on the ramp; this was done by establishing the equations of the straight line which was calculated from the graphs of root of dropping height on slope against range. These equations were:

Angle 34ºAngle 20ºAngle 15º

r = 0.4√h + 0.0954 r = 1.0125√h – 0.0614 r = 0.7√h -0.00018

Now if you look at these equations, you will see that the range is directly proportional to the root of h (which is the dropping height on slope). Therefore we can say that the relationship between the range of the jump achieved by the ski jumper and the dropping height on the ramp is a square root relationship.

Bibliography:

Modern physics – by Frederick E. Trinklein (information about GPE and KE)

http://www.physics.uoguelph.ca/tutorials/torque/Q.torque.inertia.html (RKE equation)

http://physics.about.com/cs/puzzles/a/070603_2.htm (information about RKE)

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This student written piece of work is one of many that can be found in our GCSE Height and Weight of Pupils and other Mayfield High School investigations section.

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