1.

a stone is dropped from a hundred metre cliff. What is the velocity of the stone after 3 seconds ? When does the stone hit the ground? With what velocity does the stone hit the ground?​

Answer»

ANSWER:

GIVEN:

Height = 100 metres

Initial Velocity = 0 m/s

To find:

  • Velocity of stone after 3 SECONDS
  • Velocity with which stone hits the ground
  • TIME after which the stone hits ground

Calculation:

Velocity after 3 seconds:

\therefore \: v = u + gt \\ = > v = 0 \: + 10 \times 3 \\ = > v = 30 \: metres \:{s}^{-1}

Velocity on reaching ground:

\therefore \: {v}^{2} = {u}^{2} + 2gh \\ = > {v}^{2} = {0}^{2} + 2 \times 10 \times 100 \\ = > {v}^{2} = 2000 \\ = > v = \sqrt{2000 } \\ = > v = 44.72 \: m {s}^{ - 1}

Time after which body reaches ground :

\therefore \: h = ut + \frac{1}{2} a {t}^{2} \\ = > 100 = 0 + \frac{1}{2} \times 10 \times {t}^{2} \\ = > {t}^{2} = 20 \\ = > t = \sqrt{20} \\ = > t = 4.47 \: sec.


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