SOLUTION: h(t)= -16t^2+dt+c At time t=0, a rocket was launched upward from an initial height of 6 feet. Until the rocket hit the ground, its height, in feet, after t seconds was gi

Question 630072: h(t)= -16t^2+dt+c

At time t=0, a rocket was launched upward from an initial height of 6 feet. Until the rocket hit the ground, its height, in feet, after t seconds was given by the function h aobve, in which c and d are positive constants. If the rocket reached its maximum height of 350 ft at time t=4, what was the height, in feet, of the rocket at time t=1?
(the answer is 140, by the way)
please include explanations!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
h(t)= -16t^2+dt+c
At time t=0, a rocket was launched upward from an initial height of 6 feet. Until the rocket hit the ground, its height, in feet, after t seconds was given by the function h aobve, in which c and d are positive constants. If the rocket reached its maximum height of 350 ft at time t=4, what was the height, in feet, of the rocket at time t=1?
------
h(0) = -16*0^2 + d*0 + c = 6 feet
So, c = 6
---------------------
h(4) = 350
h(4) = -16*4^2+4d + 6 = 350
256 + 4d + 6 = 350
4d = 88
d = 22
------
Equation:
h(t) = -16t^2 + 22t + 6
h(1) = -16 + 22 + 6
h(1) = 12 feet
=====================
Cheers,
Stan H.
RELATED QUESTIONS
JP launches a rocket straight upwards from a height of 20 feet above the ground with an... (answered by ikleyn,addingup)

JP launches a rocket straight upwards from a height of 20 feet above the ground with an... (answered by Alan3354)

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

A rocket is launched with an initial upward velocity of 320 feet per second from an... (answered by Alan3354)

A rocket is propelled upward from the top of a building 220 feet tall at an initial... (answered by josmiceli)

Hugh Betcha launched a model rocket with an initial speed of 88 feet per second. After... (answered by amarjeeth123)

h(t)= c-(d-4t)^2 At time t=0, a ball was thrown upward from an initial height of 6... (answered by solver91311)