Technology required. Two rocks are launched straight up in the air. The
height of Rock A is given by the function f, where f(t) = 4 + 30t – 16t2. The
height of Rock B is given by g, where g(t) = 5 + 20t – 16t2. In both
functions, t is time measured in seconds and height is measured in feet.
Use graphing technology to graph both equations. Determine which rock
hits the ground first and explain how you know.

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abidemiokin abidemiokin · Answer 1 · 2022-03-07T10:25:16+01:00

The rock that hits the ground first will be the one with lowest time that is rock B

Given the height of Rock A by the function f, where f(t) = 4 + 30t – 16t^2

Also, for the rock B, the function g(t) = 5 + 20t – 16t^2

The rock will hit the ground at f(t) = g(t) = 0

Substituting the values into the function, we will have:

4 + 30t – 16t^2 = 0

On factorizing the time taken to reach the ground is 2secs

For the function g(t) = 5 + 20t – 16t^2

0= 5 + 20t – 16t^2

On factorizing the time taken to reach the ground is 0.625secs

Hence the rock that hits the ground first will be the one with lowest time that is rock B

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