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) = - 16t^2 + 22t + 172. Approximately how high is the bridge above the ground? After how many seconds docs the ball hit the ground? After how many seconds docs the ball reach its maximum height above the ground? What is the maximum height above the ground reached by the ball?

Explanation / Answer

here,

height of ball ,

h = -16 t^2 + 22 t + 172

a)

at t = 0

height = 172 feet

the bridge is 172 feet

b) at h = -16 t^2 + 22 t + 172

for time t

as h = 0

0 = -16 t^2 + 22 t + 172

solving for t

t = 4.04 s

the time taken to reach ground is 4.04 s

c)

dh/dt = d/dt(-16 t^2 + 22 t + 172 )

dh/dt = -32 * t + 22

at maximum height dh/dt = 0

0 = -32 * t + 22

t = 0.69 s

the time taken to reach maximum height is 0.69 s

d)

for the height

h = -16 t^2 + 22 t + 172

h = -16 * 0.69^2 + 22 * 0.69 + 172

h = 179.6 feet

the maximum height is 179.6 feet

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.