SOLUTION: The function f(t) =-5t2 + 20t + 60 models the approximate height of an object t seconds after it is launched. How many seconds does it take the object to hit the ground? So that'

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The function f(t) =-5t2 + 20t + 60 models the approximate height of an object t seconds after it is launched. How many seconds does it take the object to hit the ground? So that'      Log On


   

Question 874241: The function f(t) =-5t2 + 20t + 60 models the approximate height of an object t seconds after it is launched. How many seconds does it take the object to hit the ground?
So that's the question and I am totally lost. Would you mind explaining? *I am reviewing out a textbook, I am trying to get help our teacher said it was fine to ask people how to do it if your not understanding. Thank you.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Plug in f(t) = 0. We do this because f(t) represents the height and a height of 0 means you're at the ground.

f(t) =-5t^2 + 20t + 60

0 = -5t^2 + 20t + 60

-5t^2 + 20t + 60 = 0

Now solve for t using the quadratic formula

Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for t:


Starting with the general quadratic


at%5E2%2Bbt%2Bc=0


the general solution using the quadratic equation is:


t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve -5%2At%5E2%2B20%2At%2B60=0 ( notice a=-5, b=20, and c=60)





t+=+%28-20+%2B-+sqrt%28+%2820%29%5E2-4%2A-5%2A60+%29%29%2F%282%2A-5%29 Plug in a=-5, b=20, and c=60




t+=+%28-20+%2B-+sqrt%28+400-4%2A-5%2A60+%29%29%2F%282%2A-5%29 Square 20 to get 400




t+=+%28-20+%2B-+sqrt%28+400%2B1200+%29%29%2F%282%2A-5%29 Multiply -4%2A60%2A-5 to get 1200




t+=+%28-20+%2B-+sqrt%28+1600+%29%29%2F%282%2A-5%29 Combine like terms in the radicand (everything under the square root)




t+=+%28-20+%2B-+40%29%2F%282%2A-5%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




t+=+%28-20+%2B-+40%29%2F-10 Multiply 2 and -5 to get -10


So now the expression breaks down into two parts


t+=+%28-20+%2B+40%29%2F-10 or t+=+%28-20+-+40%29%2F-10


Lets look at the first part:


x=%28-20+%2B+40%29%2F-10


t=20%2F-10 Add the terms in the numerator

t=-2 Divide


So one answer is

t=-2




Now lets look at the second part:


x=%28-20+-+40%29%2F-10


t=-60%2F-10 Subtract the terms in the numerator

t=6 Divide


So another answer is

t=6


So our solutions are:

t=-2 or t=6




Ignore the negative t value (negative time values make no sense)

The only practical solution is t+=+6

So it takes 6 seconds for the object to hit the ground.