Question

A child throws a ball straight up. If the ball is to reach a height of 9.8 m, what is the minimum initial velocity that must be imparted to the ball? Assume the initial height of the ball is 1 m. (Provide the answer to 3 decimal places and show work.)

Answer 1

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:

$s(t) = 4.9t^2 + v(0)t + s(0)$

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:

$s_{MAX} = \frac{v(0)^2 - 4(4.9)s(0)}{2(4.9)}$

In this problem:

• The initial height is of 1 m, hence $s(0) = 1$.

• A height of 9.8 m is reached when $S_{MAX} = 9.8$, hence:

$s_{MAX} = \frac{v(0)^2 - 4(-4.9)s(0)}{2(4.9)}$

$9.8 = \frac{v(0)^2 - 4(4.9)}{2(4.9)}$

$v(0)^2 - 19.6 = 96.04$

$v(0)^2 = 115.64$

$v(0) = \sqrt{115.64}$

$v(0) = 10.754$

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 brainly.com/question/24737967