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a projectile is fired from the earth surface of radius R with velocity "kv"(v=escape velocity from the earth surface and k

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 ------------

Grade:12

1 Answers

vikas askiitian expert
509 Points
11 years ago

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)

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