a) the baton is 114.8 meters above the ground.
b) after 9.8 seconds.
c) The highest point is reached after 4.9 seconds.
d) 120.8 meters.
e) No, it can't.
How high is the baton after 6 seconds?
We know that the height is modeled by the quadratic equation below:
h(t) = −gt² + vt + s
Where:
g = gravity = 4.9m/s^2
v = initial velocity = 48m/s
s = initial height = 3.2 m
Replacing all that, we get:
h(t) = -(4.9m/s^2)*t^2 + 48m/s*t + 3.2m
Where you can remove the units so it is easier to read, but I wrote them so you can understand what each term means.
First we want to find the height after 6 seconds.
The function is written as:
h(t) = -4.9*t^2 + 48*t + 3.2
Here we need to replace the variable "t" by 6, so we get:
h(6) = -4.9*6^2 + 48*6 + 3.2 = 114.8
This means that after 6 seconds, the baton is 114.8 meters above the ground.
b) The baton will return to the same height when:
h(t) = 3.2 = -4.9*t^2 + 48*t + 3.2
Solving that for t:
0 = -4.9*t^2 + 48*t
0 = t*(-4.9*t + 48)
The first solution is t = 0 which is trivial, the second one is:
0 = (-4.9*t + 48)
4.9*t = 48
t = 4.9/48 = 9.8
This means that the baton will return to the initial height after 9.8 seconds.
c) The highest point is at the vertex of the parabola:
h(t) = -4.9*t^2 + 48*t + 3.2
Which is at:
t = -48/(2*4.9) = 4.9s
The highest point is reached after 4.9 seconds.
d) h(4.9) = -4.9*4.9^2 + 48*4.9 + 3.2 = 120.8
The height at that time is 120.8 meters.
e) No, the maximum height of the baton is 120.8 meters.
If you want to learn more about quadratic equations:
https://brainly.com/question/1214333
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