SOLUTION: The height of a projectile launched upward at a speed of 32 feet/second from a height of 48 feet is given by the function: h(t)=-16t^2+32t+48. How long will it take the projectile

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The height of a projectile launched upward at a speed of 32 feet/second from a height of 48 feet is given by the function: h(t)=-16t^2+32t+48. How long will it take the projectile       Log On


   

Question 1153458: The height of a projectile launched upward at a speed of 32 feet/second from a height of 48 feet is given by the function: h(t)=-16t^2+32t+48. How long will it take the projectile to hit the ground?
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The height of a projectile launched upward at a speed of 32%28ft%2Fs%29 from a h=48 feet is given by the function:
h%28t%29=-16t%5E2%2B32t%2B48 How long will it take the projectile to hit the ground?
the projectile will hit the ground when h%28t%29=0
0=-16t%5E2%2B32t%2B48 ......factor
0=-16%28t%5E2-2t-3%29
0=-16%28t%5E2-3t%2Bt-3%29
0=-16%28%28t%5E2-3t%29%2B%28t-3%29%29
0=-16%28t%28t-3%29%2B%28t-3%29%29
0=-16%28%28t%2B1%29%28t-3%29%29
we need only positive solution for the time

t=3
Therefore, the time is +3s

Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.

Your basic equation is

    h(t) = -16t^2 + 32t + 48.



The projectile will hit the ground when h(t) = 0.



Thus the equation to solve is

    -16t^2 + 32t + 48 = 0.    (1)


You can simplify this equation SIGNIFICANTLY dividing both sides by -16. 

You will get an EQUIVALENT equation

    t^2 - 2t - 3 = 0.    (2)


The term "EQUIVALENT" means that it has the same roots as equation (1).


Now you can factor equation (2) easily  (and MENTALLY)

    (t-3)*(t+1) = 0.


The roots are  t= 3  and  t= -1, and only  positive root t= 3 is meaningful.


ANSWER.  The projectile will hit the ground in 3 seconds.


Solved.