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13 August, 14:02

Solve using the best method:

A football is punted into the air. Its height

h, in meters, after t seconds is given by the

equation h = - 4.912 + 24.5t + 1. When

does the ball hit the ground?

+3
Answers (2)
  1. 13 August, 14:41
    0
    Answer: After 5.02 seconds

    Step-by-step explanation:

    The correct equation in the question is h = - 4.912 t² + 24.5t + 1

    Hi, when the ball hits the ground, height = 0.

    So, replacing in the equation:

    0 = - 4.912 t² + 24.5t + 1

    For: ax2 + bx + c

    x = [ - b ± √b²-4ac] / 2a (quadratic formula)

    Replacing with the values given:

    x = [ - 24.5 ± √24.5²-4 (-4.912) 1] / 2 (-4.912)

    x = [ - 24.5 ± √600.25+19.648] / -9.824

    x = [ - 24.5 ± √619.898] / -9.824

    x = [ - 24.5 ± 24.90] / -9.824

    Positive:

    x = [ - 24.5 + 24.90 ] / -9.824 = - 0.04 seconds

    Negative:

    x = [ - 24.5 - 24.90] / -9.824 = 5.02 seconds

    Since time can't be negative, the answer is 5.02 seconds.

    Feel free to ask for more if needed or if you did not understand something.
  2. 13 August, 15:34
    0
    Step-by-step explanation:

    Question not written well

    The equation of the ball is meant to be in a parabola or trajectory form.

    So, h = - 4.912t² + 24.5t + 1

    The ball will hit the ground when the height is 0

    I. e. h = 0

    Therefore,

    -4.912t² + 24.5t + 1 = 0

    Using almighty formula,

    a = - 4.912 b = 24.5 c = 1

    t = (-b±√b²-4ac) / 2a

    t = (-24.5±√24.5²-4*-4.912 * 1) / 2 * - 4.912

    t = (-24.5±√600.25 + 19.648) / 9.824.

    t = (-24.5 ± 24.898) / 9.824

    So,

    t = (-24.5 + 24.898) / 9.824

    t = 0.398 / 9.824

    t = 0.04seconds

    Or

    t = (-24.5 - 24.898) / 9.824

    t = - 5.03 seconds

    So, we are going to discard the negative time,

    t = 0.04 second is the correct time the ball will hit the ground
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