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Math Help - I need help with these two problems.

  1. #1
    corey3915
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    I need help with these two problems.

    3). Suppose you throw a baseball straight up at a velocity of 64 feet per second. A function can be created by expressing distance above the ground, s, as a function of time, t. This function is s = 16t2 + v0t + s0

    16 represents 1/2g, the gravitational pull due to gravity (measured in feet per second2).
    V0 is the initial velocity (how hard do you throw the object, measured in feet per second).
    S0 is the intitial distance above ground (in feet). Ifyou are standing on the ground, then s0 = 0.

    a) What is the function that describes this problem?

    Answer:

    b). The ball will be how high above the ground after 1 second?

    Answer:
    Show work in this space.

    c). How long will it take to hit the ground?
    Answer:
    Show work here.

    d). Wha is the maximum height of the ball? What time will the maximum height be attained?

    Answer:

    Show work here.

    4. John haas 300 feet of lumber to frame a rectangular patio ( the perimeter of a rectangle is 2 times length plus 2 times width). He wants to maximize the area of his patio (area of a rectangle is length times width). What should the dimensions of the patio be?
    Answer:
    Show work in this space.

    These are the problems I need assistance with like yesterday, LOL.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by corey3915
    3). Suppose you throw a baseball straight up at a velocity of 64 feet per second. A function can be created by expressing distance above the ground, s, as a function of time, t. This function is s = 16t2 + v0t + s0

    16 represents 1/2g, the gravitational pull due to gravity (measured in feet per second2).
    V0 is the initial velocity (how hard do you throw the object, measured in feet per second).
    S0 is the intitial distance above ground (in feet). Ifyou are standing on the ground, then s0 = 0.

    a) What is the function that describes this problem?

    Answer:

    b). The ball will be how high above the ground after 1 second?

    Answer:
    Show work in this space.

    c). How long will it take to hit the ground?
    Answer:
    Show work here.

    d). Wha is the maximum height of the ball? What time will the maximum height be attained?
    I'm sorry. I don't have time to do all of this, but I can give you a quick rundown.

    For starters, s = 16t^2 + v_0t + s_0 is both right and wrong. The key to using this equation is that we have a coordinate system, that is, a specified direction to call positive. Most people will define positive to be upward, so we need to modify the equation to reflect that the acceleration due to gravity is downward:
    s = -16t^2 + v_0t + s_0

    a) Since you are starting by throwing the ball upward, v0 will be positive. Since you are throwing from "ground level" (A common simplification in these problems is that, unless otherwise stated, all objects start from ground height. It's wrong, but that's the way most of these end up reading!), we can put s0 = 0 ft. So your equation will be:
    s = -16t^2 + 64t

    b) Just plug in t = 1 s.

    c) The ball will be back at s = 0 ft, so put s = 0 and solve for t.

    d) I don't know what level of Math you are at, so let me suggest that either you:
    1) Plot the function and graphically figure out where the max height is.

    2) Use the fact that the function is a parabola and that the max height will be at the vertex point.

    (A third way is to take the first derivative of the s(t) function and set it to zero, but if you don't know Calculus, this suggestion will be gibberish!)

    -Dan
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