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The time at which the splashdown would occur assuming the rocket will splash down into the ocean is 50.0 seconds.

Given the following data:

  • Initial time = 0 seconds
  • [tex]h(t) = - 4.9t^2 + 238t + 353[/tex]

To calculate the time at which the splashdown would occur assuming that the rocket will splash down into the ocean:

The function of time.

Mathematically, the height of the rocket launched by NASA with respect to time is given by this function:

[tex]h(t) = - 4.9t^2 + 238t + 353[/tex]

Note: The height is equal to zero (0) when the splashdown occur.

[tex]h(t) = - 4.9t^2 + 238t + 353=0[/tex]

The formula for quadratic equation.

We would solve the above quadratic equation by using the quadratic formula:

[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}[/tex]

Where:

  • a = -4.9
  • b = 238
  • c = 353

Substituting the given parameters into the formula, we have;

[tex]t = \frac{-238\; \pm \;\sqrt{238^2\; - \;4(-4.9)(353)}}{2(-4.9)}\\\\t = \frac{-238\; \pm \;\sqrt{56644\; + \;6,918.8}}{-9.8}\\\\t = \frac{-238\; \pm \;\sqrt{63562.8}}{-9.8}\\\\t = \frac{-238\; \pm \;252.12}{-9.8}\\\\t = \frac{-490.12}{-9.8}[/tex]

Time, t = 50.0 seconds.

Read more on time here: https://brainly.com/question/24728358