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

Click here to see ALL problems on Travel Word Problems

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