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Kinematic

December 17, 2007

A gun G fires a shell with initial speed V at an angle Θ above the horizontal. The shell hits a target T which is a distance d horizontally from G and a distance h below it. Given there is only one possible value for theta for which this occurs, show that

V² = g ( – h + ( h² + ( h² + d² ) )

(Adapted from A-Level Further Maths, Specimen Paper 1)

 

Well, I had a hard time solving this…crack my head, paid Chew a visit…just to discover that this question is meant to punish those who are thinking too much. 😦

I and Chew discussed the question for about an hour…poor Chew, he had to rush to the cinema after spending too much time on that question. He was the one who found the key to the question….

Initially I tried eliminating the parameter t, and the equation turn became a nasty trigonometry equation…..urgh…I thought I need knowledge on further trigonometry to solve that (which is, unnecessary, of course.)

It is simple, really. Look for equations for horizontal and vertical motion, then eliminate Θ as a parameter rather than t.

Have fun! Can be solved at SPM level. If you don’t make the same mistake as me 🙂

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