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How High Did It Fly?
Hanna Pretorius
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.
Background
We found two ways in which to solve the
problem (both based on similar triangles):
 Trigonometry
 Scale
Drawings
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.
M
sin M = opp/hyp
h
a
cos M = adj/hyp
tan M = opp/adj
o
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.
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.
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
Problems experienced

Construction of inclinometer

Testing the inclinometer (mistakes in
measuring)

Windy launch days

Rocket launcher not straight
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.
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.
?
Angle of elevation
was 74º
10 m
The End!!!