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A ballistic missile is launched from a fighter jet flying at a height of 40 m from the ground. The missile hits the tank which is present on the ground. The function h(t) = -8t^2 + 32t +40h(t) represents the height (in meters) of the missile after t seconds.
Assume the dimension of the tank and the fighter jet is negligible.
*Find out the maximum height(in meters) attained by the missile.
*Find out the time (in seconds) when the missile hits the tank.
*Suppose an air defense system is present at the origin, and it follows the straight line path h(t) = 10t, find the height from the ground at which the air defense missile will destroy the ballistic missile in the air.

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raphealnwobi

The maximum height attained by the missile is 72 meters, the missile hit the tank at 5 seconds and the air defense missile will destroy the ballistic missile is 4 second.

What is an equation?

An equation is an expression that shows the relationship between two or more variables and numbers.

Given that:

h(t) = -8t² + 32t + 40

The maximum height is at h'(t) = 0, hence:

-16t + 32 = 0

t = 2 s

h(2) = -8(2)² + 32(2) + 40 = 72 meter

The time the missile hit the tank is at h(t) = 0, hence:

0 = -8t² + 32t + 40

t = 5 s

For the air defense system:

-8t² + 32t + 40 = 10t

t = 4 s

The maximum height attained by the missile is 72 meters, the missile hit the tank at 5 seconds and the air defense missile will destroy the ballistic missile is 4 second.

Find out more on equation at: https://brainly.com/question/2972832

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