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. 
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Your equation is:
h(t)= -16t^2+Vot+ho
h(t)= -16t^2+120t+10
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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
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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
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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
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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