Answer
$(250, -50,0)$ ; $10\sqrt{93} m/s \approx 96.4 ft/s$
Work Step by Step
Use velocity-time equation.
$v=u+at$
$v=u+(\lt0,-4,-32 \gt \lt 50,0,80 \gt)t$
$v=\lt 50,-4t,80-32t \gt$
$r(t)=\int v(t)=\lt 50t,-2t^2,80t-16t^2 \gt$
Since, $80t=16t^2=0$
$t=5$
Thus,
$r(5)=\lt 50(5),-2(5)^2,80(5)-16(5)^2 \gt=\lt 250, -50,0 \gt$
$v(5)=\lt 50, -20,-80 \gt$
Thus, final speed is $|v(5)|=\sqrt {(50)^2+( -20)^2+(-80)^2 }=\sqrt {100+400+6400}=10\sqrt{93} m/s \approx 96.4 ft/s$
