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Let the mass of the body be M. It is thrown up with a velocity of 10 m/s, but returns to the ground with a velocity of 9 m/s.
It means that in upward and downward journey it lost energy due to dissipative forces equal to kinetic energy of 1m/s, i.e. it lost energy equivalent to kinetic energy of ½ m/s either way.
So it is equivalent to saying that it was thrown up with an initial velocity of 9.5 m/s, rather than 10m/s, and forget about dissipative forces.
At the highest point the entire kinetic energy is converted into potential energy. Let the height achieved be h. Then
½ m v² = m g h,==> h = v²/2g = 9.5²/2×9.8= 4.61 m.
The body shall achieve a height of 4.61 m.
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