The function f gives the height of a ball, h, above the ground (measured in feet

Question

The function f gives the height of a ball, h, above the ground (measured in feet) in terms of the number of seconds elapsed since the ball was thrown upward from a bridge that is some distance above the ground, t. Let h f(t) and f(t)-162 35t+ 164 a. Approximately how high is the bridge above the ground? feet Preview b. After how many seconds does the ball hit the ground? seconds after the ball was thrown Preview c. After how many seconds does the ball reach its maximum height above the ground? secondsPreview d. What is the maximum height above the ground reached by the ball? feet above the ground Preview

Explanation / Answer

f(t) = -16t^2 + 35t + 164

a) plugging t = 0 in the equation

f(t) = 16(0)^2 + 35(0) + 164

h = 164

so, bridge is 164 feet high above the ground

b) plugging f(t) = 0

-16t^2 + 35t + 164 = 0

t = 4.5 seconds

the ball will hit the ground after 4.5 seconds

c) the ball will reach maximum height after

t = -35 / 2(-16) = 1.094 seconds

d) maximum height

h = -16(1.094)^2 + 35(1.094) + 164

h = 183.141 feet

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