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a projectile is fired vertically upwards and reaches a height of 0.0125 km find the velocity of projection and time takes it to reach its highest point |
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Answer» rojectile is fired vertically upwards from the earth's surface with a velocity v and reaches a height h. Energy of the PROJECTILE at the surface of the earth is E i = 21 MV 2 − R E GM E m Energy of the projectile at a height h E f =− R E +hGM E m (∴ At height h velocity of the projectile is zero.)According to law of conservation of energy, E i =E f 21 mv 2 − R E GM E m =− R E +hGM E m 21 mv 2 =GM E m[ R E 1 − R E +hI ]= (R E )(R E +h)GM E MH 21 mv 2 = R E +hmghR E (∵g= R E2 GM E )As per question,v=kv e =K 2gR E (∵v e = 2gR E )and h=r−R E ∴ 21 mk 2 2gR E = rmg(r−R E )R E k 2 = rr−R E ⇒(I−k 2 )r=R E ⇒r= 1−k 2 R E |
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