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SCALCET$92\mathrm{.}1\mathrm{.}005.$

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The deck of a bridge is suspended $265$ feet above a river. If a pebble falls off the side of the bridge, the height, in feet, of the pebble above the water surface after $t$ seconds is given by $y=265-16t^2.$

$($a$)$ Find the average velocity $($in $f\frac{t}{s})$ of the pebble for the time period beginning when $t=4$ and lasting the following amount of time.

$($i$)0\mathrm{.}1$ seconds

$f\frac{t}{s}$

$($ii$)0\mathrm{.}05$ seconds

$f\frac{t}{s}$

$($iii$)0\mathrm{.}01$ seconds

$f\frac{t}{s}$

$($b$)$ Estimate the instantaneous velocity $($in $f\frac{t}{s})$ of the pebble after $4$ seconds.

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