SOLUTION: if a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second, then its height h after t seconds is given by the equation h(t)= -1

Question 893761: if a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second, then its height h after t seconds is given by the equation h(t)= -16t[square] +128t (if air resistence is neglected). How long will it take for the rocket to return to the ground? After how many seconds will the rocket be 112 feet above the ground? how long will it take the rocket to hit its maximum height? What is the maximum height?
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
if a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second, then its height h after t seconds is given by the equation h(t)= -16t[square] +128t (if air resistance is neglected). How long will it take for the rocket to return to the ground? After how many seconds will the rocket be 112 feet above the ground? how long will it take the rocket to hit its maximum height? What is the maximum height?
***
h(t)= -16t^2 +128t
returning to ground:
0=-16t(t-8)
t=0
or
t=8
How long will it take for the rocket to return to the ground? 8 sec
..
112 ft above ground:
112=-16t^2+128t
-16t^2+128t-112=0
-t^2+8t-7=0
(-t+1)(t-7)=0
t=1
or
t=7
After how many seconds will the rocket be 112 feet above the ground? after 1 sec on the way up and after 7 sec on the way down
..
maximum height
h(t)= -16t^2 +128t
complete the square:
h(t)= -16(t^2 -8t+16)+256
h(t)=-16(t-4)^2+256
This is an equation of a parabola that opens downwards with vertex at (4,256)
Rocket will reach its maximum height of 256 ft 4 sec after launch

RELATED QUESTIONS
A toy rocket is launched vertically upward from ground level with an initial velocity of... (answered by Boreal)

If a rocket is launched vertically upward from ground level with an initial velocity of... (answered by CubeyThePenguin)

A toy rocket is launched upward from ground level with an initial velocity of 39 meters... (answered by lwsshak3)

This is from a worksheet from Glencoe Algebra 1. Mr Adim's science class launched a toy... (answered by longjonsilver,Earlsdon)

A rocket is launched straight up from the ground with an initial velocity of 96 feet per... (answered by Alan3354)

a toy rocket is launched from a 144- foot cliff overlooking the ocean with an initial... (answered by jsmallt9)

Mr. Alim's science class launched a toy rocket from ground level with an initial upward... (answered by solver91311)

Height of a Projectile A projectile is fired straight upward from ground level with an... (answered by ankor@dixie-net.com)

A toy rocket is launched from the ground with an initial velocity of 80 feet per second.... (answered by stanbon)