Answers

2014-06-07T21:44:22+08:00
Problem:

"An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. What will be the object's maximum height? When will it attain this height?"

The initial height is 80 feet above ground and the initial speed is 64 ft/s. Since the units are "feet", then the number for gravity will be 16, and the equation is:
s(t) = –16t2 + 64t + 80
For a negative quadratic like this, the maximum will be at the vertex of the upside-down parabola. From graphing, to find the vertex; in this case, the vertex is at (2, 144):
h = –b/2a = –(64)/2(–16) = –64/–32 = 2 
k = s(2) = –16(2)2 + 64(2) + 80 = –16(4) + 128 + 80 = 208 – 64 = 144
According to the equation, plugging in time values and extracting height values, so the input "2" must be the time and the output "144" must be the height.

It takes two seconds to reach the maximum height of 144 feet.
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