SOLUTION: A bottle rocket is launched vertically upward with a velocity of 120 feet per secound from a back porch deck that is 10 feet off of the ground. Use the formula h(t)= -16t^2+Vot+ho
Algebra.Com
Question 456070: A bottle rocket is launched vertically upward with a velocity of 120 feet per secound from a back porch deck that is 10 feet off of the ground. Use the formula h(t)= -16t^2+Vot+ho to answer the following questions. A)How high is the rocket after 3 seconds? B)how long does it take for the rocket to hit the ground? C)how long does it take the rocket to reach its highest distance above the ground? D) what is the highest distance above the ground that the rocket reaches?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
A bottle rocket is launched vertically upward with a velocity of 120 feet per secound from a back porch deck that is 10 feet off of the ground. Use the formula h(t)= -16t^2+Vot+ho to answer the following questions.
.
Your equation is:
h(t)= -16t^2+Vot+ho
h(t)= -16t^2+120t+10
.
A)How high is the rocket after 3 seconds?
set t to 3 and solve:
h(3)= -16(3)^2+120(3)+10
h(3)= -16(9)+360+10
h(3)= -144+360+10
h(3)= 226 feet
.
B)how long does it take for the rocket to hit the ground?
set h(t) to 0 and solve for t:
h(t)= -16t^2+120t+10
0= -16t^2+120t+10
dividing both sides by -2:
0= 8t^2-60t-5
solve by applying the quadratic formula to get:
t = {7.58, -0.08}
throw out the negative solution leaving
t = 7.58 seconds
.
C)how long does it take the rocket to reach its highest distance above the ground?
h(t)= -16t^2+120t+10
since the coefficient associated with the x^2 term is negative, we know that it is a parabola that opens downwards -- which means the vertex is the max
t = -b/(2a)
t = -120/(2(-16))
t = -120/(-32)
t = 3.75 seconds
.
D) what is the highest distance above the ground that the rocket reaches?
set to to 3.75 to find out:
h(3.75) = -16(3.75)^2+120(3.75)+10
h(3.75) = 235 feet
RELATED QUESTIONS
A bottle rocket is launched vertically upward with a velocity of 120 feet per secound... (answered by stanbon)
A bottle rocket is launched vertically upward with a velocity of 130 feet per secound... (answered by stanbon)
Suppose a bottle rocket is launched upward with a velocity of 96 feet a second, and from... (answered by ikleyn)
Suppose that a bottle rocket is launched upward with a initial velocity of 96ft/sec from... (answered by ikleyn)
If a rocket is launched vertically upward from ground level with an initial velocity of... (answered by CubeyThePenguin)
A rocket is launched upward with a velocity of 64 feet per second from the top of a fifty (answered by Alan3354)
A rocket is launched upward with a velocity of 288 feet per second from the top of a... (answered by rothauserc,Alan3354)
A rocket is launched with an initial upward velocity of 320 feet per second from an... (answered by Alan3354)
If a rocket is launched from Houston, Texas, with an initial velocity of 1600 feet per... (answered by stanbon)