24.8 m/s
Explanation:
You don't have to solve for time first. You can use the equation below to solve for the velocity before impact:
[tex]v_y^2 = v_{0y}^2 + 2a_yy[/tex]
We know that [tex]v_{0y} = 0[/tex] so the equation above becomes
[tex]v_y^2 = 2a_yy \Rightarrow v_y = \sqrt{-2a_yy}[/tex]
Plugging in the numbers, we get
[tex]v_y = \sqrt{-2(-9.8\:\text{m/s}^2)(31.3\:\text{m})}[/tex]
[tex]\:\:\:\:\:=24.8\:\text{m/s}[/tex]
METHOD 2:
If you insist on using that equation for d, we can do that too. So solving for t from the equation for d. we get
[tex]t = \sqrt{\dfrac{2d}{g}} = \sqrt{\dfrac{2(31.3\:\text{m})}{9.8\:\text{m/s}^2}}[/tex]
[tex]\:\:\:\:= 2.53\:\text{s}[/tex]
So using the equation [tex]v_y = gt,[/tex] we get
[tex]v_y = (9.8\:\text{m/s}^2)(2.53\:\text{s}) = 24.8\:\text{m/s}[/tex]
So you get the same result regardless of the method you use.
