A cricket ball thrown across a field is at heights $$h1$$ and $$h2$$ from the point of projection at times $$t1$$ and $$t2$$ respectively after the throw. The ball is caught by a fielder at the same height as that of projection. The time of flight of the ball in this journey is [WB JEE $$2014$$]

Question

A cricket ball thrown across a field is at heights $$h1$$ and $$h2$$ from the point of projection at times $$t1$$ and $$t2$$ respectively after the throw. The ball is caught by a fielder at the same height as that of projection. The time of flight of the ball in this journey is                             [WB JEE $$2014$$]

Infinity Learn · Accepted Answer

For vertical motion,   $$h1=usin$$θ$$t1-12gt12$$      (For$$ $$h1)⇒  $$t1=h1+12gt12usin$$θ           ………(i)⇒  $$h2=usin$$θ$$t2-12gt22$$                               (For$$ $$h2)⇒  $$t2=h2+12gt22usin$$θ          ………(ii)On$$ dividing Eq. $$(i) by Eq. (ii), we $$gett1t2=h1+12gt12/usin$$θ$$h2+12gt22/usin$$θ⇒  $$h1t2-h2t1=g2t1t22-t12t2The$$ time of flight of the ball,$$T=2usin$$θ$$g=2g(usin$$θ$$)=2gh1+1/2gt12t1$$             [From Eq. (i)]$$=2t1h1g+t122=h1t1$$×$$2g+t1=h1t1$$×$$t1t22-t12t2h1t2-h2t1+t1=h1t1t22-ht12t2+ht12t2-h2t13t1h1t2-h2t1=h1t22-h2t12h1t2-h2t1$$

A cricket ball thrown across a field is at heights h₁ and h₂ from the point of projection at times t₁ and t₂ respectively after the throw. The ball is caught by a fielder at the same height as that of projection. The time of flight of the ball in this journey is [WB JEE 2014]

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A cricket ball thrown across a field is at heights h1 and h2 from the point of projection at times t1 and t2 respectively after the throw. The ball is caught by a fielder at the same height as that of projection. The time of flight of the ball in this journey is [WB JEE 2014]

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A cricket ball thrown across a field is at heights h₁ and h₂ from the point of projection at times t₁ and t₂ respectively after the throw. The ball is caught by a fielder at the same height as that of projection. The time of flight of the ball in this journey is [WB JEE 2014]