Question

Find the height, in feet, of the missile after 5 seconds in the air.A missile is launched from the ground. Its height, h(x), can be represented by a quadratic function in terms of time, x, in seconds.After 1 second, the missile is 243 feet in the air; after 2 seconds, it is 452 feet in the air.The height of the can be represented bythis function h(x) = - 17x2 + 260x

find the height, in feet, of the missile after 5 seconds in the air

Answer 1

The height of the missile after 5 seconds in the air is 97 feet.

Step-by-step explanation:

To find the height of the missile after 5 seconds, substitute x = 5 into the quadratic function
`\(h(x) = -17x^2 + 260x\):`

`\[h(5) = -17(5)^2 + 260(5)\]`

Simplifying this expression yields the height after 5 seconds, which is 97 feet. The quadratic function
`\(h(x) = -17x^2 + 260x\)` represents the missile's height as a function of time, with the term
`\(-17x^2\)`capturing the effect of gravity. The coefficient of
`\(x^2\)` is negative, indicating a downward-opening parabola. The positive term
`\(260x\)` represents the initial upward velocity of the missile.

By evaluating the function at
`\(x = 5\)`, we determine the height at that specific time. In this case, after 5 seconds, the missile is 97 feet in the air. The negative value of the quadratic term dominates as time progresses, leading to a decrease in height and reflecting the influence of gravity on the missile's trajectory.