How to determine when a ball will hit the ground (Factor a Polynomial) (a MATH 1010 Problem)
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The problem: A cannonball is fired from a cliff. The height s of the cannonball (in feet) as a function of time t (in seconds) can be modeled by the function:
s(t)=-16t^2+64t+260
When will the ball hit the ground?
The solution: 6.5 seconds. Since s(t) is zero when the ball hits the ground, we only need to factor the expression -16t^2+64t+260. In the video I factor out a 4 from each term, then factor the polynomial by grouping. This means that either of the two factored binomials (2t - 13) or (-2t - 5) have to equal zero, and that gives us two answers, t = 6.5 and -2.5. Since -2.5 seconds does not make sense in this problem, it cannot be an answer. Therefore 6.5 seconds is our only answer.
The first question is what is the height of the ball after 2 seconds. To solve this question, we replace t in the equation with 2 giving us:
s(2)= -16(2)^2 + 64 (2) + 260
simplified:
s(2) = -16(4) + 128 +260
simplified:
s(2) = -64 + 128 + 260
which simplifies to
s(2) = 324
therefore, the height of the cannon ball after 2 seconds is 324 feet.