Gone Forever

Classical Mechanics Level 3

I toss a stone at a velocity of \(14000 \text{ m/s}\), and an angle chosen uniformly at random from the interval \([0^\circ, 90^\circ]\), above the horizontal. What is the probability that the stone will never return to Earth?

Details and Assumptions:

  • \(g=9.8 \text { m/s}^2\), radius of Earth 6371 km.

  • Ignore other massive bodies, such as the sun.


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