A ball is thrown from ground level with initial speed v $($m$/$sec$)$ and at an angle of$$ with the

horizontal. It hits the ground at a distance$2$ sin$(2)$

$(,)$ v

s v g

$$

$=$ where$8\mathrm{.}9=$g m$/$sec$2.$

$($a$)$ Find the differentialds $.$

$($b$)$ What does the sign of$(20,3)$s

$$

$$ tell you?

$($c$)$ Use the linearization of s about$(20,3)$

$$ to estimate the change in$$ that is needed to get

approximately the same distance if the initial speed changes to $19$ m$/$sec