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Three stones A, B and C are projected from surface of very long inclined plane with equal speeds and different angles of projections as shown in figure. The incline makes an angle θ with the horizontal. If HA,HB and HC are maximum height attained by A, B and C respectively above inclined plane, then (neglect air friction)

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a

HA+HC=HB

b

HA2+HC2=HB2

c

HA+HC=2HB

d

HA2+HC2=2HB2

answer is A.

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Detailed Solution

HA=u2sin2⁡α2gcos⁡θ HB=u22gcos⁡θ HC=u2sin2⁡90-α2gcos⁡θ=u2cos2⁡α2gcos⁡θ⇒ HA+HC=HB

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Three stones A, B and C are projected from surface of very long inclined plane with equal speeds and different angles of projections as shown in figure. The incline makes an angle θ with the horizontal. If HA,HB and HC are maximum height attained by A, B and C respectively above inclined plane, then (neglect air friction)