Tanya kicks a ball into the air. The function that models this is f(t) = -16t^2 + 96t, where h is the height of the ball in feet and t is th

Question

Tanya kicks a ball into the air. The function that models this is f(t) = -16t^2 + 96t, where h is the height of the ball in feet and t is the time seconds

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Aaliyah 2 weeks 2021-09-07T22:20:46+00:00 1 Answer 0

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    2021-09-07T22:22:16+00:00

    The question is incomplete. The complete question is here.

    Tanya kicks a ball into the air. The function that models this scenario is h(t) = -16t² + 96t, where h is the height of the ball in feet and t is the time seconds. When will the ball hit the ground?

    Answer:

    The ball will hit the ground after 6 seconds

    Step-by-step explanation:

    ∵ h(t) = -16t² + 96t

    ∵ h is the height of the ball in feet for t seconds

    – That means at the ground h = 0

    ∵ h(t) = 0 when the ball hit the ground

    0 = -16t² + 96t

    Let us solve it by adding 16t² to both sides

    ∴ 16t² = 96t

    – Subtract 96t from both sides

    16t² – 96t = 0

    Factorize it by taking 16t as a common factor from each term

    ∵ 16t² ÷ 16t = t

    ∵ 96t ÷ 16t = 6

    16t(t – 6) = 0

    Equate each factor by 0

    ∵ 16t = 0

    – Divide both sides by 16

    t = 0 ⇒ initial position

    ∵ t – 6 = 0

    – Add 6 to both sides

    t = 6 ⇒ final position

    The ball will hit the ground after 6 seconds

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