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'Weekly Challenge 26: Max Throw' printed from http://nrich.maths.org/
A particle is projected with speed $10$ m $s^{-1}$ from a
flat horizontal surface. Find, with proof, the angle from which it
should be projected to maximise the distance travelled before it
hits the surface. Does this angle depend on the speed of
projection?
The particle is now projected with speed $10$ m $s^{-1}$ from
a height of $2$ metres.
From what angle (to 3sf) should it now be projected to
maximise the distance travelled before it hits the surface?
Does this angle depend on the speed of projection?
Did you
know ... ?
The modelling assumptions of constant gravitational field and no
friction opposing motion are good ones, leading to simple equations
which always have parabolas for solution. Once these modelling
assumptions are, rightly, challenged, the resulting equations
become 'non-linear' and very difficult to solve. Mathematicians
often take the parabola as a starting point to solving the more
complicated equations and vary the solution a little to try to
fit it back into the new equations. You can see an aspect of this
process in the solution to this problem.