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A water jet from a fountain reaches its maximum height of 4 m at a distance 0.5 m from the vertical passing through the point O of water outlet. The height (in m) of the jet above the horizontal $O X$ at a distance of 0.75 m from the point O is

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answer is 3.

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Detailed Solution

The path of the water jet is a parabola.
Let its equation be $y = a x^{2} + b x + c$
It should pass through $(0, 0), (0.5, 4),$ and $(1, 0)$ . Therefore,
$c = 0, a = - 16, b = 16$
$∴ y = - 16 x^{2} + 16 x$
If $x = 0.75,$ then $y = 3$ .
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A water jet from a fountain reaches its maximum height of 4 m at a distance 0.5 m from the vertical passing through the point O of water outlet. The height (in m) of the jet above the horizontal OX at a distance of 0.75 m from the point O is