word problem

Question

Gi is standing on the top of a 275 feet building. She throws a ball straight up into the air. The balls initial velocity is given as 48 ft/sec. The height, in feet, of the ball after t seconds is given by h=-16t^2+48t+275 A. How long will it take for the ball to reach its maximum height above the ground? B. What is the maximum height that the ball reaches? C. How many seconds does it take for the ball to finally hit the ground? (Round answer to the nearest tenth of a second)

Answer 1

h = -16t² + 48t + 275

 

Vertex at (-b/2a, h(-b/2a))

-b/2a = -48/-32 = 1.5

Maximum height reached at 1.5 seconds

 

h(1.5) = -16(1.5)² + 48(1.5) + 275 = 311 ft maximum height

 

-16t² + 48t + 275 = 0

Using quadratic formula...

t = [-48±√(48²-4(-16)(275))]/[2(-16)]

t =  [-48±√19904]/(-32)

t = (-48 ± 141.08)/(-32)

 

Since we know the time will be a positive quantity, we can go with

 

t = (-48 - 141.08)/(-32) = 5.91 seconds to hit the ground