Respuesta :
Given that the initial velocity is u = 25 m/s.
We have to find the final velocity and time at its maximum height.
First, we need to find the maximum height.
[tex]h\text{ =}\frac{u}{2g}[/tex]Here, g = 9.81 m/s^2 is the acceleration due to gravity.
Substituting the values, the height will be
[tex]\begin{gathered} h=\text{ }\frac{25}{2\times9.81} \\ =1.274\text{ m} \end{gathered}[/tex](a) Let the final velocity be v.
The formula to calculate final velocity is
[tex]\begin{gathered} v^2=u^2-2gh^{} \\ v=\sqrt[]{u^2-2gh^{}} \end{gathered}[/tex]Substituting the values, the final velocity will be
[tex]\begin{gathered} v=\sqrt[]{\lbrack(25)^2-(2\times9.81\times1.274)\rbrack} \\ =\sqrt[]{600.01} \\ =24.49\text{ m/s} \end{gathered}[/tex](b) The time taken can be calculated by the formula,
[tex]\begin{gathered} t=\frac{v-u}{-g} \\ =\frac{24.49-25}{-9.81} \\ =0.051\text{ s} \end{gathered}[/tex]Thus, the final velocity is 24.49 m/s and time is 0.051 s
