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rajan jha Grade: 12
        

a projectile is fired from the earth surface of radius R with velocity "kv"(v=escape velocity from the earth surface and k<1). Neglecting air resistance, the maximum height of rise from the centre of the earth is ------------

6 years ago

Answers : (1)

vikas askiitian expert
510 Points
										

initial PE = -GMm/R


(KE)i = mV2/2 = mk2v2/2


v = (2GM/R)1/2                               (escape speed = (2GM/R)1/2)


so , (KE)i = k2GMm/R


total energy initial = GMmK2/R - GMm/R         ......................1


 finally particle comes to rest after attaining a H height...


now PE = -GMm/(R+H)


     (KE)f = 0


total energy = -GMm/(R+H)                 .................2


since mechanical energy is conserved so eq1 = eq2


 -GMm/(R+H) = -GMM/R +K2GMm/R


H/R+H = K2


 H = RK2/(1-K2)

6 years ago
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