Answer: t= 4 seconds
Maximum height = 256 feet
Step-by-step explanation:
The height of the object projected upwards after t seconds is given by
s(t)=-16t^2+128t.
The expression is a quadratic equation. When this equation is plotted on a graph, height against time, it takes the shape of a parabola whose vertex represents the maximum height attained by the object.
To get the value of t at the maximum height,
t = -b/2a
From the equation,
a = -16
b = 128
t = -128/-2×-16
= -128 /- 32= 4
it will take 4 seconds to reach its maximum height
To find maximum height attained, put t= 4 in the equation
s(t)=-16t^2+128t
S = -16× 4^2 + 128×4
S = -256+512
S = 256 feet
