## anonymous one year ago will fan & medal!!!!!!!!!!!!!! 2. A model rocket is launched from the ground with an initial velocity of 288 ft/sec. c. How long will it take the rocket to reach its maximum height? Show all work in the space provided.

1. misty1212

HI!!

2. misty1212

i am guessing you are supposed to use $h(t)=-16t^2+228t$

3. misty1212

max is at the vertex first coordinate of the vertex is always $-\frac{b}{2a}$ which in your case is $-\frac{288}{2\times (-16)}$

4. anonymous

d. Assume the model rocket’s parachute failed to deploy and the rocket fell back to the ground. How long would it take the rocket to return to Earth from the time it was launched? Show all work in the space provided.

5. misty1212

set $-16t^2+288t=0$ and solve for $$t$$ takes 3 steps only

6. misty1212

or maybe two

7. misty1212

factors nicely as $-16t (t-18) = 0$

8. anonymous

another way to think about it is to simply take the derivative of the equation 'misty1212' posted which is -32t=-288 and t=288/32. to prove this, the second derivative is -32 which is < 0 therefore it is a maximum.

9. anonymous

thnx a lot guys really appreciate the help