Question 1082914
*[illustration ds4.png].
{{{X^2+Y^2=13^2}}}
{{{X^2+Y^2=169}}}
Differentiating,
{{{2X*(dX/dt)+2Y*(dY/dt)=0}}}
{{{X(dX/dt)=-Y(dY/dt)}}}
{{{dX/dt=-(Y/X)(dY/dt)}}}
When {{{X=5}}},
{{{5^2+Y^2=169}}}
{{{Y^2=169-25}}}
{{{Y^2=144}}}
{{{Y=12}}}
Substituting,
{{{dX/dt=-(12/5)(-4)}}}
{{{highlight(V=dX/dt=48/5)}}}{{{ft/s}}}
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Differntiating again,
{{{X*(d2X/dt2)+(dX/dt)^2+Y*(d2Y/dt2)+(dY/dt)^2=0}}}
Since the Y speed is constant the second derivative (Y wrt time) equals zero.
{{{5*(d2X/dt2)+(48/5)^2+12*(0)+(5)^2=0}}}
{{{5*(d2X/dt2)=-(2304/25)-25}}}
{{{d2X/dt2=-(2304/125+5)}}}
{{{highlight(a=-(2929/25))}}}{{{ft/s^2}}}