A golfer hits a ball from a starting elevation of 6 feet with a velocity of 70 feet per second down to a green with an elevation of −3 feet.

Question

A golfer hits a ball from a starting elevation of 6 feet with a velocity of 70 feet per second down to a green with an elevation of −3 feet. The number of seconds t it takes the ball to hit the green can be represented by the equation −16t2 + 70t + 6 = −3. How long does it take the ball to land on the green? It takes the ball seconds to land on the green.

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Ruby 2 months 2021-10-03T17:02:12+00:00 1 Answer 0 views 0

Answers ( )

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    2021-10-03T17:04:08+00:00

    Answer:

    The time it takes the ball to land on green is 4.4175 seconds

    Step-by-step explanation:

    Given

    Equation for number of seconds it take to hit the green: −16t² + 70t + 6 = −3

    Required

    The value of t.

    The interpretation of this question is that, we should solve for t in the above equation.

    -16t² + 70t + 6 = −3

    Collect like terms

    -16t² + 70t + 6 – 3 = 0

    -16t² + 70t + 3 = 0

    Multiply through by -1

    -1(-16t² + 70t + 3) = -1 * 0

    16t² – 70t – 3 = 0

    Solving using quadratic formula.

    t = \frac{-b+-\sqrt{b^2 - 4ac}}{2a}

    Where a = 16, b = -70, c = -3

    t = (-(-70) ± √(-70² – 4 * 16 * -3))/(2 * 16)

    t = \frac{-(-70)+-\sqrt{(-70)^2 - 4 * 16 * -3}}{2 * 16}

    t = (70 ± √(4900 + 192))/32

    t = \frac{70+-\sqrt{4900 + 192}}{32}

    t = \frac{70+-\sqrt{5092}}{32}

    t = \frac{70+-71.36}{32}

    t = \frac{70+71.36}{32} or t = \frac{70-71.36}{32}

    t = \frac{141.36}{32} or t = \frac{-1.36}{32}

    t = 4.4175 \\ or\\ t =-0.0425

    But t can’t be negative.

    So, t = 4.4175

    The time it takes the ball to land on green is 4.4175 seconds

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