M3 circular motion Watch

Jordan97
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Could someone please explain to me why the horizontal component of the velocity is used in part c, surely we should be looking at the vertical component if we are trying to find the maximum height?
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Onlineslayer
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Yes
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Onlineslayer
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The second to the last equation ...in lay term simply says;

The energy due to the additional rise in height (I.e extra potential energy)
Plus
The unchanging kinetic energy due to a constant horizontal velocity (k.e using only horizontal component)

Will be equal to;
The kinetic energy currently possessed by the particle (I.e the k.e using the present actual velocity).


The philosophy here is that the only reason the particle will fall down again is because the vertical component of velocity will be converted to potential energy increase. The horizontal component however remains fixated.
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