Feel the Gravity

Two balls of mud are hurtling above the Earth, as shown below.

The balls collide at a height of \(4R_E\) from the surface of the Earth, stick together, and start to fall straight down toward the Earth. Find the time (in seconds) it takes for the composite mudball to reach the surface of the Earth.

Details and Assumptions:

  • The mud balls move with speed \(\SI{512}{\meter/\second}\) just before collision.
  • The radius of the Earth is \(R_E = \SI{6400}{\kilo\meter}.\)
  • \(\theta = 60^\circ.\)
  • The mass of the Earth is \(M_E = \SI{6e24}{\kilo\gram}.\)
  • \(G = \SI[per-mode=symbol]{6.67e-11}{\newton\meter\squared\per\kilo\gram\squared}.\)
  • Ignore the effect of wind resistance. \[\] -This problem is Original ! :)
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