word problem

Question

 a ball falls off the top of a roof 320 feet above the ground. the formula h=-16t² + 16t +320 describes the height of the ball above the ground, h, in feet,t, seconds after the ball begins. how long will it take the ball to hit the ground?

Answer 1

You are given

 

h(t) = -16t² + 16t + 320

 

The ball hits the ground when

 

h(t) = 0

 

Then

 

-16t² + 16t + 320 = 0

 

Solve this quadratic equation for t, and the positive solution will be the time in seconds it takes to hit the ground.

 

Now note there is an error in the problem statement.  The first sentence should say "A ball is tossed vertically upward at a speed of 16 feet per second."  The ball does not fall off the roof.  If it did, the equation for h(t) would be

 

h(t) = -16t² + 320

Answer 2

-16t² + 16t + 320 = 0

 

Note that all terms here are divisible by 16 so you can reduce

this quadratic to:

 

-16(t² - t  - 20) = 0

divide both sides by -16

t² - t - 20 = 0

 

The factors of -20 that add to -1 are (-5)(4)

So your equation factors to:

(t-5)(t+4) = 0

 

t-5 = 0     or    t+4 = 0

t = 5 secs  or   t = -4 secs

 

Since the time will not be negative

 

t = 5 seconds