Algebra 2 Word Problem

Question

Fireworks are discharged vertically upward from a height of 4 feet above the ground. Its path is given by,

h = -16t2 + 160t + 4, where h is the height of the fireworks in feet and t is time in seconds. When will the debris hit the ground?

Answer 1

the debris hits the ground when the 

height is 0

 

0 = -16t² + 160t + 4

 

solve the quadratic equation

by using the quadratic formula:

 

t =[ - 160 ± √( 160² - 4(-16)(4))] / -32

 

t = -320.79/-32

 

t = 10.02 seconds

 

 

Answer 2

The height as a function of time is given by h(t) = -16t² + 160t + 4.

 

Neglecting air resistance, the debris reaches the ground when h(t) = 0.  You will have a quadratic equation in time.  Solve for t.  You will get two solutions.  One will be physically unrealistic, such as a negative time.  The other will be the time elapsed from when the rocket was launched from a height of 4 feet above the ground, until the debris reaches the ground at a height of 0 feet.