A falling object has a velocity function, in $\frac{ft}{sec},$ given by $v(t)=-32t.$ If its initial height is $160$ feet, how high will it be after $3$ seconds? $($Hint: Use the graph of the velocity function to calculate how far the object falls in $3$ seconds.$)$

$($A$)36$ ft

$($B$)16$ ft

$($C$)48$ ft

$($D$)32$ ft

$($E$)24$ ft