Answer
$(250, -50,0)$ ; $10\sqrt{93} m/s \approx 96.4 ft/s$
Work Step by Step
$v=u+(\lt0,-4,-32 \gt \lt 50,0,80 \gt)t$ [ velocity-time equation, that is $v=u+at$]
Thus, $v=\lt 50,-4t,80-32t \gt$
Also, $r(t)=\int v(t)=\lt 50t,-2t^2,80t-16t^2 \gt$
Equate the equations such as: $80t=16t^2=0$
This yields, $t=5$
Now, $r(5)=\lt 50(5),-2(5)^2,80(5)-16(5)^2 \gt$
or, $r(5)=\lt 250, -50,0 \gt$
This yields:$v(5)=\lt 50, -20,-80 \gt$
Need to find the final speed.
$|v(5)|=\sqrt {(50)^2+( -20)^2+(-80)^2 }$
or, $=\sqrt {100+400+6400}$
or, $=10\sqrt{93} m/s $
or, $\approx 96.4 ft/s$
