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Q.

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

u1cos⁡α=u2cos⁡β303=u22sin⁡2βg⇒303=u2232g⇒ u22=600 or u2=106t2=2u2sin⁡60∘g=2(106)3/210⇒t2=18u1=106cos⁡60∘cos⁡30∘=102−h=102sin⁡30∘18−1210(18)2 =30−90⇒h=60m
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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