Recall that
[tex]{v_f}^2-{v_i}^2=2a\Delta y[/tex]
We're given [tex]v_i=1.00\,\frac{\mathrm m}{\mathrm s}[/tex], [tex]a=-0.37\,\frac{\mathrm m}{\mathrm s^2}[/tex] (so we take the upward direction to be positive), and [tex]\Delta y=0.79\,\mathrm m[/tex]. Then the final velocity [tex]v_f[/tex] satisfies
[tex]{v_f}^2-\left(1.00\,\dfrac{\mathrm m}{\mathrm s}\right)^2=2\left(-0.37\,\dfrac{\mathrm m}{\mathrm s^2}\right)(0.79\,\mathrm m)[/tex]
[tex]\implies {v_f}^2=0.42\,\dfrac{\mathrm m^2}{\mathrm s^2}[/tex]
[tex]\implies v_f=0.64\,\dfrac{\mathrm m}{\mathrm s}[/tex]
