Respuesta :
Answer:
256
Step-by-step explanation:
Read the answer carefully and then you'll know hey i need to multiply 8 times 32.
And what do you get...... 256
Modeling the situation with a quadratic equation, it is found that:
- The maximum height of the ball is of 60.2 feet.
- The ball hits the ground after 3.39 seconds.
Considering the gravity, the height of the ball, after t seconds, is given by the following quadratic equation.
[tex]h(t) = -4.9t^2 + v_0t + h_0[/tex]
In which:
- [tex]v_0[/tex] is the initial velocity.
- [tex]h_0[/tex] is the initial height.
In this problem:
- Height of 8 feet, thus [tex]h_0 = 8[/tex].
- Initial velocity of 32 feet per second, [tex]v_0 = 32[/tex]
The equation is:
[tex]h(t) = -4.9t^2 + 32t + 8[/tex]
Which is a quadratic equation with [tex]a = -4.9, b = 32, c = 8[/tex].
The maximum height is the output of the vertex, which is:
[tex]h_{MAX} = -\frac{\Delta}{4a} = -\frac{b^2 - 4ac}{4a}[/tex]
Then, with the coefficients of this question:
[tex]h_{MAX} = -\frac{32^2 - 4(-4.9)(8)}{4(-4.9)} = 60.2[/tex]
The maximum height of the ball is of 60.2 feet.
It hits the ground at t for which [tex]h(t) = 0[/tex], thus:
[tex]\Delta = b^2 - 4ac = 32^2 - 4(-4.9)(8) = 1180.8[/tex]
[tex]t_{1} = \frac{-32 + \sqrt{1180.8}}{2(-4.9)} = -0.12[/tex]
[tex]t_{2} = \frac{-32 - \sqrt{1180.8}}{2(-4.9)} = 3.39[/tex]
We want the positive value, so:
The ball hits the ground after 3.39 seconds.
A similar problem is given at https://brainly.com/question/24626341
