Question

NASA launches a test rocket with an initial velocity of 235 meters per second from an initial height of 15 meters above sea-level. Find a quadratic function that models the height of the rocket, in meters above sea-level, as a function of time t , in seconds after the launch. (HINT: 4.9 meters = 16 feet) Use your model to answer the following questions. Assuming that the rocket will splash down into the ocean, how many seconds after launch does splashdown occur? (round to the nearest tenth of one second) The rocket splashes down after seconds. What is the maximum height above sea-level attained by the rocket? (round to the nearest meter) The maximum height is meters above sea-level.

Answer 1

9514 1404 393

Answer:

• 48.0 seconds
• 2833 meters

Explanation:

A graphing calculator shows the points of interest nicely.

The rocket splashes down after 48.0 seconds.

The maximum height is 2833 meters above sea level.

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The equation for the motion is ...

h(t) = -4.9t^2 +235t +15 . . . . launch at 235 m/s from height of 15 m

The vertex (maximum height) is found at ...

t = -(235)/(2(-4.9)) = 235/9.8 ≈ 23.980 . . . seconds

Then the maximum height is ...

h(23.980) = (-4.9(23.980) +235)(23.980) +15 ≈ 2833 . . . meters

The value of t when h(t) = 0 can be found using the quadratic formula.

t = (-235 -√(235² -4(-4.9)(15)))/(2(-4.9)) = (-235 -√55519)/-9.8

t ≈ 48.023 ≈ 48.0 . . . seconds