Answer:
Step-by-step explanation:
a)The height h after t seconds is given by the equation h(t)=-16t^2+112t+5.
Where 5 represents 5feet above the ground and this is the height from which the rocket was launched.
The equation is a quadratic equation. The plot of this equation on a graph would give a parabola whose vertex would be equal to the maximum height travelled by the rocket.
The vertex of the parabola is calculated as follows,
Vertex = -b/2a
From the equation,
a = -16
b = 112
Vertex = - - 112/32= 3.5
So the rocket will attain maximum height at 3.5 seconds.
It will also take 3.5 seconds to reach the ground. This means it will take a total of 3.5 seconds + 3.5 seconds
= 7 seconds to hit the ground.
b) to find time it will take to be 100 feet above the ground,
-16t^2+112t-95 = 0
Using general quadratic equation formula,
a = -16
b = 112
c = -95
t = [-b+/-√b^2-4ac]/2a
t = [ -112 +/-√112^2-4×-16×-95]/16 × -2
= [-112 +/-√12544-6080]/-32
= (-112+80.4)/-32 or (-112-80.4)/-32
t = 0.9875 or t = 6.0125
So it will take 0.9875 or approximately 1 second to be 100 feet above the ground
