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Standard IX

Mathematics

Vertically Opposite Angles

Two projectil...

Question

Two projectiles A and B are projected with same velocity u. They cover the same horizontal range. If A is thrown at an angle 15 degree with the horizontal , what is the angle of projection of B?

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Solution

$W e k n o w t h e h o r i z o n t a l r a n g e i s g i v e n b y; H = \frac{2 u^{2}}{g} \sin θ . \cos θ I n t h e g i v e n c a s e o n e o f t h e p r o j e c t i l e i s t h r o w n w i t h a n a n g l e 15 ° i . e . H = \frac{2 u^{2}}{g} s i n 15 ° c o s 15 ° t h e r e f o r e o t h e r p r o j e c t i l e i s p r o j e c t e d w i t h a n g l e; ϕ = (\frac{π}{2} - 15 °) f o r s a m e h o r i z o n t a l r a n g e . T h e r e f o r e t h e n e w h o r i z o n t a l r a n g e = H' = \frac{2 u^{2}}{g} \sin (\frac{π}{2} - 15 °) . \cos (\frac{π}{2} - 15 °) H' = \frac{2 u^{2}}{g} s i n 15 ° c o s 15 ° T h u s H = H'$

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