Given
x: Horizontal distance
x = 8 m
y: vertical distance
y = 11 m
Hit the target at the peak of the trajectory
Procedure
Let's first make a diagram of the situation.
Projectile Motion
Parabolic motions can be analyzed as the superposition of a horizontal motion and a vertical motion. Let's first analyze the vertical movement, which is very similar to free fall. Recall that the maximum point of the velocity at y is equal to 0 and from here we can calculate the y-component of the velocity.
![\begin{gathered} v^2_(fy)=v^2_(oy)-2gy \\ 0=v^2_(oy)-2gy \\ v_(oy)=\sqrt[]{2\cdot g\cdot y}_{} \\ v_(oy)=\sqrt[]{2\cdot9.8\cdot6} \\ v_(oy)=10.84\text{ m/s} \end{gathered}](https://img.qammunity.org/2023/formulas/physics/college/dbnkdz8f16qyt080nyay61waezzo2cda2a.png)
Now we can calculate the time it takes to go to the maximum point.

Finally we can calculate the velocity in x

We have the x and y components of the initial velocity. Now we can calculate the magnitude and the angle.
![\begin{gathered} v^2_o=v^2_(ox)+v^2_(oy) \\ v_o=\sqrt[]{10.84^2+7.22^2} \\ v_o=13.03\text{ m/s} \end{gathered}](https://img.qammunity.org/2023/formulas/physics/college/v4cvupoc7gliky3erikvi7a1lzfj74jn0h.png)
