Question

The escape velocity of a bullet from the surface of planet Y is 1759.0 m/s. CALCULATE the escape velocity from the surface of the planet X if the mass of planet X is 1.59 times that of Y, and its radius is 0.895 times the radius of Y.

Answer 1

Use gravitational PE

At surface of Planet Y
PEy = -mGMy/Ry
KE.escape = 1/2m Vy^2
KE = PE.infinity - PEy
1/2 mV.y^2 = mGMy/Ry
Vy = ?(2GMy/Ry)

At surface of Planet X
PEx = -GMx/Rx
Vx = ? (2GMx/Rx)

Vx/Vy = ? (2GMx/Rx) / ?(2GMy/Ry)
Vx= Vy ? (Mx/My *Ry/Rx)
Vx = Vy ? (1.59/.895)

Vx = 1759* ? (1.59/.895)
Vx = 2345 m/s

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Answer 2

IT MAY BE HELPFUL

Replace the value as given and get the exact correct answer .

1.21 ----> 1.59 and

0.823 ----->0.895