The equation of motion of a projectile is y $$=$$ $$ax-bx2$$ where a and b are constants of motion. Match the quantities of Column $$-$$ I with the relations of Column $$-$$ II and mark the correct choice from the given codes.Codes

Question

The equation of motion of a projectile is y $$=$$ $$ax-bx2$$ where a and b are constants of motion. Match the quantities of Column $$-$$ I with the relations of Column $$-$$ II and mark the correct choice from the given codes.Codes

Infinity Learn · Accepted Answer

Comparing given equation, y $$=$$ $$ax-bx2$$ with the equation of projectile motiony $$=$$ x $$tan$$ θ$$-$$ $$gx22u2cos2$$θWe get, $$tan$$ θ $$=$$ $$a-------(i)$$       g $$sec2$$θ$$2u2$$ $$=$$ $$b----(ii)or$$ $$u2$$ $$=$$ $$g(1+tan2$$θ$$)2b$$ $$=$$ $$g(1+a2)2b$$    (Using$$ $$(i)or$$ u $$=$$ [$$g(1+a2)2b$$]Here $$i-s$$.Horizontal range $$=$$ $$u2sin2$$θg $$=$$ $$2u2sin$$θ $$cos$$θ g                          $$=$$ $$=$$ $$2u2cos2$$θg×$$tan$$θ $$=$$ ab                                               $$(Using$$ $$(i) and (ii))Hence$$ $$ii-p$$.Maximum height $$=$$ $$u2sin2$$θ$$2g$$ $$=$$ $$u2cos2$$θ$$2g$$×$$tan2$$θ                          $$=$$ $$2u2cos2$$θ$$4g$$×$$tan2$$θ $$=$$ $$a24b$$                                              $$(Using$$ $$(i) and (ii))Hence$$ $$iii-r$$.From $$(ii), b $$=$$ $$g2u2cos2$$θor $$u2cos2$$θ $$=$$ $$g2b$$ or u $$cos$$ θ $$=$$ $$g2b$$          (iii)Time$$ of flight $$=$$ $$2u$$ $$sin$$ θ$$g=2gu$$ $$cos$$θ× $$tan$$θ                    $$=$$ $$2gg2b$$×a $$=$$ $$a2bg$$                                           $$(Using$$ $$(i) and $$(iii))Hece$$ $$iv-q$$

The equation of motion of a projectile is y = ax-bx2 where a and b are constants of motion. Match the quantities of Column - I with the relations of Column - II and mark the correct choice from the given codes.Codes

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