Answer
$|\textbf{V}_{x}|=|\textbf{V}_{y}|=850\,ft/s$
Work Step by Step
Magnitude of the horizontal component $|\textbf{V}_{x}|=|\textbf{V}|\cos\theta=1200\,ft/s\times\cos 45^{\circ}=850\,ft/s$
Magnitude of the vertical component
$|\textbf{V}_{y}|=|\textbf{V}|\sin\theta=1200\,ft/s\times\sin 45^{\circ}=850\,ft/s$
(Both are equal because $\sin 45^{\circ}=\cos 45^{\circ}$)
