Question

Some fireworks are fired vertically into the air from the ground at an initial speed of 80 feet per second. The equation for this object’s height h at time t seconds after launch is
h= -16t^2 + 80t
How long will it take the fireworks to reach the ground?

Answer 1

Answer:

The firework will take 5 s to reach the ground again.

Step-by-step explanation:

For the firework to reach the ground it's height must be equal to 0, so we need to solve the given equation for t with h=0. We have:

h = -16t² + 80t

0 = -16t² + 80t

16t² -80t = 0

t(16t - 80) = 0

In this case we have an incomplete second order equation, there are only two values that can satisfy that equality, these are given bellow:

t = 0 s

16t - 80 = 0

16t = 80

t = 80/16 = 5 s

Since 0 s is when it was launched, then 5 s is the time it takes to reach the ground again.

Answer 2

Answer:

5 sec

Step-by-step explanation:

The equation for this object’s height h at time t seconds after launch is

h= -16t²+ 80t

According to the given problem, height would be zero for the firework to reach the ground, therefore, we are required to  find time 't' when h=0. We get:

0 = -16t² + 80t

16t² -80t = 0

t(16t - 80) = 0

EITHER : t = 0 s

OR : 16t - 80 = 0 =>16t = 80

t = 80/16 = 5 s

Since t=0 s is not possible because that would mean the fireworks are not fired yet

Therefore,  it will take 5s to the fireworks to reach the ground