Question - Calculating Resultant Vector Magnitude

The given vectors form the legs of a right triangle with one vector pointing East with a magnitude of \( 24.0 \, m \) and the other pointing North with a magnitude of \( 14.0 \, m \).

Using the equation for the magnitude of the resultant vector \( c = \sqrt{a^2 + b^2} \), where \( a \) and \( b \) are the magnitudes of the individual vectors:

\( c = \sqrt{(24.0 \, m)^2 + (14.0 \, m)^2} \)

\( c = \sqrt{576.0 \, m^2 + 196.0 \, m^2} \)

\( c = \sqrt{772.0 \, m^2} \)

\( c \approx 27.8 \, m \)

The magnitude of the resultant vector is approximately \( 27.8 \, m \).