Question

5. The Riverside Geyser in Yellowstone National Park erupts

about every 6.25 h. When the geyser erupts, the water has an
initial upward velocity of 69 ft/s.
A. Use the vertical motion model h = -16t2 + vt + c to write
an equation that model this situation.
B. Then find the maximum height of the geyser?
Round your values to the nearest foot.
A. Use the vertical motion model h=-16t2+vt+c to write an equation that model this situation B. Then find the maximum height of the geyser

Answer 1

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

__

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.