Answer:
3 seconds
Explanation:
The initial velocity is 60 m/s at an angle of 30° to the horizontal, so we can calculate the initial velocity in the vertical direction as
Viy = Vi sin(θ)
Viy = 60 sin(30)
Viy = 60(0.5)
Viy = 30 m/s
Then, we can use the following equation to calculate the time that it takes to reach the maximum height.
[tex]\begin{gathered} v_{fy}=v_{iy}-gt \\ v_{fy}+gt=v_{iy} \\ gt=v_{iy}-v_{fy} \\ \\ t=\frac{v_{iy}-v_{fy}}{g} \end{gathered}[/tex]At a maximum height the vertical velocity is 0 m/s, so replacing viy = 30 m/s, vfy = 0 m/s and g = 10 m/s², we get
[tex]\begin{gathered} t=\frac{30\text{ m/s-0m/s}}{10\text{ m/s}^2} \\ \\ t=\frac{30\text{ m/s}}{10\text{ m/s}^2} \\ \\ t=3\text{ s} \end{gathered}[/tex]Therefore, the answer is 3 seconds
