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math

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a baseball is hit with an initial velocity of 75 feet per second from the height of 3 feet.
The function h(t)=-16t squared + 75t + 3 models the path of the baseball where t represents the time in seconds that the ball has been traveling and h represents the height of the ball at time t.
1) after how many seconds is the height of the ball is 79.5 feet?
2) how long will it take for the ball to return to the ground?
3) how long will it take the ball to reach its maximum height? What is the mazimum height reached?

  • math -

    1. h = 16t^2 + 75t + 3 = 79.5 Ft.
    -16t^2 + 75t -76.5 = 0.
    Use Quadratjc Formula and get:
    t = = 1.5 s.

    2. d = Vo*t + 0.5g*t^2 = 90.9 Ft.
    0 + 16*t^2 = 90.9.
    t^2 = 90.9 / 16 = 5.68.
    Tf = 2.38 s. = Fall time.

    T = Tr + Tf = 2.34 + 2.38 = 4.72 s. =
    Time in flight or time to return to gnd.


    3a. Tr = (Vf-Vo)/g.
    Tr = (0-75) / -32 = 2.34 s. = Rise time

    3b. hmax=-16*(2.34)^2 + 75*2.34+3=90.9
    Ft.

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