1. How High Did It Fly? Hanna Pretorius

2. Rocket Scientists Need Help Mlungisi and John asked us to work out how high their rocket flew. They needed to know this because they had to work out what the average speed of their rocket was.

3. Background We found two ways in which to solve the problem (both based on similar triangles): Trigonometry Trigonometry Scale Drawings Scale Drawings

4. Trigonometry We found out that, in a right-angled triangle, the ratios of sides remain constant for similar triangles, and that these are related to angles inside these triangles. These constant ratios have names. a o h sin M = opp/hyp cos M = adj/hyp tan M = opp/adj M

5. Using Trigonometry The application becomes easy then. A calculator is programmed with all the ratios for every angle. To solve, you just need two bits of information. Angle of elevation Distance on ground from rocket launch pad ? After having drawn a mathematical sketch of the situation, we can then use the ratio tan to solve the problem.

6. Scale Drawings The same sketch can also be used with scale. Scale the distance from the launch pad on graph paper, plot the angle of elevation and then, by construction, find the height of the rocket on the plan. Using the chosen scale you can work it back to find the actual height the rocket flew.

7. Measuring Instrument We decided on an inclinometer as the best (and most affordable) option for measuring angles of elevation. © The Exploratorium, www.exploratorium.edu Source: www.exploratorium.edu/math_explorer/howHigh_makeInclino.html www.exploratorium.edu/math_explorer/howHigh_makeInclino.html

8. Problems experienced Construction of inclinometer Construction of inclinometer Testing the inclinometer (mistakes in measuring) Testing the inclinometer (mistakes in measuring) Windy launch days Windy launch days Rocket launcher not straight Rocket launcher not straight

9. So the rocket went up… 36,4 metres We used both methods (to double check ourselves), but we will only show the trig calculations. We also took the average angle of elevation of three successful launchings: 72º, 75º and 75º.

10. Angle of elevation was 74º 10 m ? Height of rocket’s flight = 10 m x tan 74º = 34,9 m But since the angle was measured from a height of 1,5 m, the final height of the rocket’s flight was 36,4 m.

11. The End!!!