If the angle of projection of a projector with same initial velocity exceed or fall short of $$45$$° by equal amount α, then the ratio of horizontal ranges is [Kerala CEE $$2014$$]

Question

If the angle of projection of a projector with same initial velocity exceed or fall short of $$45$$° by equal amount α, then the ratio of horizontal ranges is                             [Kerala CEE $$2014$$]

Infinity Learn · Accepted Answer

Given,  θ$$1$$ $$=$$ θ$$2$$ $$=$$ $$450$$θ$$1$$ $$+$$ θ$$2$$ $$=$$ (450$$ $$+$$ α$$) $$+$$ (450$$ $$-$$ α$$) $$=$$ $$900u1$$ $$=$$ $$u2$$ $$=$$ u  ⇒ $$R1$$ $$=$$ $$R2$$ $$=$$ ?$$R1=u12sin$$θ$$1+$$θ$$2g$$⇒  $$R1=u2sin90$$°$$g=u2g$$                 ……..$$(i)Similarly$$,  $$R2=u22sin$$θ$$1+$$θ$$2g$$⇒ $$R2=u2sin90$$°$$g=u2g$$                ……..$$(ii)The$$ ratio of horizontal $$rangesR1R2=u2/gu2/g=1$$:$$1$$⇒  $$R1$$:$$R2=1$$:$$1$$

If the angle of projection of a projector with same initial velocity exceed or fall short of 45° by equal amount $α$ , then the ratio of horizontal ranges is [Kerala CEE 2014]

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If the angle of projection of a projector with same initial velocity exceed or fall short of 45° by equal amount α, then the ratio of horizontal ranges is [Kerala CEE 2014]

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If the angle of projection of a projector with same initial velocity exceed or fall short of 45° by equal amount $α$ , then the ratio of horizontal ranges is [Kerala CEE 2014]