A model airplane is shot up from a platform 1 foot above the ground with an initial upward velocity of 56 feet per second. The height of the airplane above ground after t seconds is given by the equation h=-16t^+56t+1, where h is the height of the airplane in feet and t is the time in seconds after it is launched. Approximately how long does it take the airplane to reach its maximum height?
A.
0.3 seconds
B.
1.8 seconds
C.
3.5 seconds
D.
6.9 seconds
feet units drive me crazy but all right.
16 t^2 - 56 t - 1 = -h
16 t^2 - 56 t = - h + 1
t^2 - 3.5 t = - h/16 + 1/16
t^2 - 3.5 t + (3.5/2)^2 = -h/16 + 1/16 + 12.25/4
(t - 3.5/2)^2 = ......
vertex (top) when t = 3.5/2 = 1.75 seconds
if they ask how high, keep going with completing the square.
By the way, if you happen to know Physics:
v = Vi - 32 t
at top t = 0
0 = 56 - 32 t
t = 1.75 seconds
By the way, if you happen to know Physics:
v = Vi - 32 t
at top v = 0
0 = 56 - 32 t
t = 1.75 seconds
32 ft/sec^2 = acceleration of gravity in these obsolete units
To find the time it takes for the airplane to reach its maximum height, we need to find the vertex of the quadratic equation representing the height of the airplane.
The equation for the height of the airplane is given as h = -16t^2 + 56t + 1, where h represents the height in feet and t represents the time in seconds.
The vertex of a quadratic equation in the form of h = at^2 + bt + c, can be found using the formula t = -b/2a.
In this case, a = -16 and b = 56. Plugging these values into the formula, we can find the time it takes for the airplane to reach its maximum height.
t = -56 / (2 * -16)
t = -56 / -32
t = 1.75 seconds
Therefore, approximately the time it takes for the airplane to reach its maximum height is 1.8 seconds.
Therefore, the answer is B. 1.8 seconds.