Question

A missile is launched from the ground. Its height,h(x) can be represented by a qyadratic function in terms of time, x, in seconds after 1 second the missile is 103 feet in the air; after 2 seconds it is 192 feet in the air. Find the height in feet of the missile after 5 seconds in the air

Answer 1

375 ft

Explanation:

The increase in height in the 1st second is 103 ft. In the 2nd second, it is 192-103 = 89 ft, a decrease of 14 ft. In the next three seconds, the increases in height can be expected to be ...

89 -14 = 75 ft

75 -14 = 61 ft

61 -14 = 47 ft

for a total increase in height over those 3 seconds of ...

75 + 61 + 47 = 183 ft

Then the height after 5 seconds in the air is ...

192 ft + 183 ft = 375 ft

_____

You can model the height function with the quadratic equation ...

h(t) = at^2 +bt

We need to find the values of "a" and "b", which we can do by substituting the given data point values. The given data is ...

h(1) = a + b = 103

h(2) = 4a + 2b = 192

Subtracting twice the first equation from the second, we get

(4a +2b) -2(a +b) = (192) -2(103)

2a = -14 . . . . . simplify

a = -7 . . . . . . . divide by 2

b = 103 -a = 110 . . . . find b using the first equation

Then the quadratic model of height is ...

h(t) = -7t^2 +110t

and the height at 5 seconds is ...

h(5) = -7·25 +110·5 = 375 . . . feet