The instantaneous height and position of a projectile are given by $x = 6 t, y = 8 t - 5 t^{2}$ meter, the initial speed of the projectile, in m/s is ______. (‘t’ is in sec)

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answer is 10.

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Detailed Solution

x = 6t
$∴ \frac{d x}{d t} = 6$
$y = 8 t - 5 t^{2}$
$∴ \frac{d y}{d t} = 8 - 10 t$ at $t = 0, \frac{d y}{d t} = 8$
Initial velocity = $\sqrt{6^{2} + 8^{2}} = 10 m / s$

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