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1st Equation of Motion

Q. Two projec...

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Q. Two projectile are thrown with different velocities and at different angles so as to cover the same max. height. Show that the sum of the times taken by each to reach the highest point is equal to the total time taken by either of the projectiles.

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Solution

Dear Student,

$L e t t i m e t a k e n b y 1 s t a n d 2 n d p r o j e c t i l e b e t_{1} & t_{2} f o r c o v e r i n g t h e i r r e s p e c t i v e m a x i m u m h i e g h t s, h_{1} & h_{2} . L e t i n i t i a l v e l o c i t i e s o f 1 s t a n d 2 n d p r o j e c t i l e b e v & u a n d θ & ϕ b e t h e a n g l e s o f p r o j e c t i o n r e s p e c t i v e l y . T h e n A c c o r d i n g t o t h e q u e s t i o n : h_{1} = h_{2} \frac{v^{2} \sin^{2} θ}{2 g} = \frac{u^{2} s i n^{2} ϕ}{2 g} v^{2} s i n^{2} θ = u^{2} s i n^{2} ϕ v s i n θ = u \sin ϕ (1) A l s o, t_{1} + t_{2} = \frac{v \sin θ}{g} + \frac{u \sin ϕ}{g} u \sin g (1) h e r e, w e g e t : t_{1} + t_{2} = \frac{2 v s i n θ}{g} = \frac{2 u s i n ϕ}{g} o r, t_{1} + t_{2} = T_{1} = T_{2} W h e r e, T_{1} & T_{2} a r e t h e t o t a l t i m e p e r i o d s o f f l i g h t o f p r o j e c t i l e 1 & 2 r e s p e c t i v e l y .$

Regards,
Manoj Singh

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