The vertical distance covered by the feather is,
[tex]h=ut+\frac{1}{2}gt^2[/tex]
As the feather is falling freely therefore, the initial speed of the feather is zero.
Substitute the known values and solve to calculate the time taken.
[tex]\begin{gathered} 89.0\text{ m=(0 m/s)t+}\frac{1}{2}(9.8m/s^2)t^2 \\ t^2=\frac{2(89.0\text{ m)}}{(9.8m/s^2)} \\ t=\sqrt[]{18.16s^2} \\ \approx4.26\text{ s} \end{gathered}[/tex]
Therefore, the time for which the feather remain in the air is 4.26 s.
The final speed of the feather can be given as,
[tex]v=u+gt[/tex]
Substitute the known values,
[tex]\begin{gathered} v=0m/s+(9.8m/s^2)(4.26\text{ s)} \\ \approx41.75\text{ m/s} \end{gathered}[/tex]
Therefore, the speed with which it strikes on the ground is 41.75 m/s.
