Question

Two gymnasts are running toward each other in a floor routine, and they plan to precisely time a flip to stay synchronized for the audience. The path of the gymnasts is parabolic and modeled by the following equations, where y is the height of the flip and x is the time in seconds.
= – (x – 5)2 + 3
y = –3(x –6)2 + x + 1
2seconds
3seconds
4seconds
5seconds

Answer 1

To make sure the flip is in unison after 4  seconds should the flip occur, as given by option C: 4 seconds.

We have given that,

Two gymnasts are running toward each other in a floor routine, and they plan to precisely time a flip to stay synchronized for the audience.

What does synchronized motion mean?

Synchronized motion is a motion of two or more system which goes in synchronization with each other.

For this case, the flip will occur such that both gymnasts are synchronized and the flip is in unison (simultaneous).

For that, we need the time(x) and the height (y) same.

Since the motion paths are:

$y=-(x-5)^2+3$

$y=-3(x-3)^2+x+1$

Therefore, we need to find the values of x for which the same y comes as output.

Let x =  t be the time for which the height y is the same, then:

$-(t-5)^2+3=-3(t-3)^2+t+1$ = height achieved by both gymnasts.

Solving it further:

$-(t-5)^2+3=-3(t-3)^2+t+1$

t=4,t=1/2

Assuming they planned to do a flip after an integral number of time in seconds, the correct option is t = 4 seconds.

Thus, to make sure the flip is in unison after 4  seconds should the flip occur, as given by the option C: 4 seconds.

Learn more about solving a system of equations here:

brainly.com/question/2825832

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