Question

5. The Riverside Geyser in Yellowstone National Park erupts

Answer 1

Answer:

Step-by-step explanation:

A.

The equation for the model of the geyser is found by substituting the given upward velocity into the vertical motion model. The problem statement tells us v=69. We assume the height is measured from ground level, so c=0. Putting these values into the model gives ...

  h(t) = -16t² +69t

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B.

The maximum height is at a time that is halfway between the zeros of the function.

  h(t) = -16t(t -4.3125) . . . . . has zeros at t=0 and t=4.3125

The maximum height will occur at t=4.3125/2 = 2.15625 seconds. The height at that time is ...

  h(t) = -16(2.15625)(2.15625 -4.3125) = 16(2.15625²) ≈ 74.39 . . . feet

The maximum height of the geyser is about 74.4 feet.