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The height of a projectile launched upward at a speed of 32 feet/second from a height of 128 feet is given by the function h(t) = -16t^2 + 32t +128. How long will it take the projectile to hit the ground?

User Seasoned
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1 Answer

4 votes

Answer:

It takes 4 seconds for the projectile to hit the ground

Explanation:

The height of the projectile after t seconds is given by the following equation:


h(t) = -16t^(2) + 32t + 128

How long will it take the projectile to hit the ground?

It happens when
h(t) = 0

So


h(t) = -16t^(2) + 32t + 128


-16t^(2) + 32t + 128 = 0

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:


ax^(2) + bx + c, a\\eq0.

This polynomial has roots
x_(1), x_(2) such that
ax^(2) + bx + c = a(x - x_(1))*(x - x_(2)), given by the following formulas:


x_(1) = (-b + √(\bigtriangleup))/(2*a)


x_(2) = (-b - √(\bigtriangleup))/(2*a)


\bigtriangleup = b^(2) - 4ac

In this question:


-16t^(2) + 32t + 128 = 0

So
a = -16, b = 32, c = 128


\bigtriangleup = 32^(2) - 4*(-16)*(128) = 9216


t_(1) = (-32 + √(9216))/(2*(-16)) = -2


t_(2) = (-32 - √(9216))/(2*(-16)) = 4

Time is a positive measure, so:

It takes 4 seconds for the projectile to hit the ground

User Changwang Zhang
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