Respuesta :
Using quadratic function concepts, it is found that the minimum initial velocity that must be imparted to the ball is of 10.754 m/s.
What is the equation of motion?
The equation of motion of an object thrown upwards, considering the effect of the gravity, is given by:
[tex]s(t) = 4.9t^2 + v(0)t + s(0)[/tex]
In which:
- v(0) is the initial velocity.
- s(0) is the initial height.
What is the maximum height obtained?
The maximum height obtained is the output of the vertex, which is given by:
[tex]s_{MAX} = \frac{v(0)^2 - 4(4.9)s(0)}{2(4.9)}[/tex]
In this problem:
- The initial height is of 1 m, hence [tex]s(0) = 1[/tex].
- A height of 9.8 m is reached when [tex]S_{MAX} = 9.8[/tex], hence:
[tex]s_{MAX} = \frac{v(0)^2 - 4(-4.9)s(0)}{2(4.9)}[/tex]
[tex]9.8 = \frac{v(0)^2 - 4(4.9)}{2(4.9)}[/tex]
[tex]v(0)^2 - 19.6 = 96.04[/tex]
[tex]v(0)^2 = 115.64[/tex]
[tex]v(0) = \sqrt{115.64}[/tex]
[tex]v(0) = 10.754[/tex]
The minimum initial velocity that must be imparted to the ball is of 10.754 m/s.
You can learn more about quadratic function concepts at https://brainly.com/question/24737967
