Shots are fired simultaneously from the top and bottom of a vertical cliff with the elevation α=30∘, β=60∘,respectively (Figure). The shots strike an object simultaneously at the same point. If a=303m is the horizontal distance of the object from the cliff, then the height h of the cliff is
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a
30 m
b
45 m
c
60 m
d
90 m
answer is C.
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Detailed Solution
u1cosα=u2cosβ303=u22sin2βg⇒303=u2232g⇒ u22=600 or u2=106t2=2u2sin60∘g=2(106)3/210⇒t2=18u1=106cos60∘cos30∘=102−h=102sin30∘18−1210(18)2 =30−90⇒h=60m
Shots are fired simultaneously from the top and bottom of a vertical cliff with the elevation α=30∘, β=60∘,respectively (Figure). The shots strike an object simultaneously at the same point. If a=303m is the horizontal distance of the object from the cliff, then the height h of the cliff is