A rocket shoots up 123 meters.  What is its initial velocity?

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The rocket is shot upwards and reaches a maximum height of 123 m.

Let the initial velocity at which the rocket is shot upwards be equal to v m/s.

The gravitational potential energy of the rocket when it is shot up is equal to 0. The kinetic energy is equal to (1/2)*m*v^2 where m is the mass of the rocket.

At a height of 123 m, the rocket has come to a stop and its kinetic energy is 0. The gravitational potential energy of the rocket is m*9.8*123.

Total energy in a closed system is conserved. This gives:

0 + (1/2)*m*v^2 = m*9.8*123 + 0

=> v^2 = 19.6*123

=> v = 49.09 m/s

The initial velocity of the rocket is 49.09 m/s

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