# A model rocket with a mass of 2.7kg is launched straight up from the ground at a speed of 110m/s. How high is the rocket when it is flying at 22.92m/s?

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Mar 8, 2018

#### Answer:

the rocket will reach a height of approx. 578 meters.

#### Explanation:

the rocket starts with a velocity 110 m/s .

So it has Initial kinetic energy

KE(1) = **1/2 x mass x ( 110m/s.)^2**

after reaching certain height say h

its velocity is reduced to

22.92 m/s ,its kinetic energy is now

KE(2) = **1/2 x mass x (22.92)^2 (m/s)^2**

the rocket must have reached to a height h where it has acquired a Potential energy in the Earth's gravitational field taking surface of earth as reference.

**P.E. = mass xg x h**

by conservation of energy this potential energy must be equal to the difference in kinetic energy of the rocket.

therefore

PE = KE(1) - KE(2)

**mass x g x h = 1/2 . mass ( 110 x110 - 22.92 x 22.92) (m/s)^2**

calculate h= (110x110 -22.92x22.92) / 2.g

one can take g =10 m/s^2

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