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Math Help - Calculus 3 - Range and Height Problem

  1. #1
    Member VitaX's Avatar
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    Calculus 3 - Range and Height Problem

    A shot leaves a thrower's hand 6.5 feet above the ground. The angle at which it was thrown is 45 degrees and it had a velocity of 44 \frac{ft}{s}. Find the time it hits the ground and the range.

    The equations are as follows:

    x=x_o + (V_o cos\theta)t ; y=y_o + (V_o tsin\theta - \frac{1}{2} gt^2)

    So basically what I have to do is, set the y equation equal to t and find a t value. Then plug that t value in for the x equation. Here's my work

    y=(\frac{-g}{2})t^2 + (V_o sin\theta)t + y_o which is in (At^2 + Bt + C = 0) format.

    t=\frac{V_o sin\theta + \sqrt{(V_o sin\theta)^2 + 2gy_o}}{g}

    Subbed my values in and I got t=2.1348 s

    Plugged that value for t in the x equation and got 66.4194 ft. How does my equation look for finding t? If its right then I think I can assume my values for t and x are correct as well.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by VitaX View Post
    A shot leaves a thrower's hand 6.5 feet above the ground. The angle at which it was thrown is 45 degrees and it had a velocity of 44 \frac{ft}{s}. Find the time it hits the ground and the range.

    The equations are as follows:

    x=x_o + (V_o cos\theta)t ; y=y_o + (V_o tsin\theta - \frac{1}{2} gt^2)

    So basically what I have to do is, set the y equation equal to t and find a t value. Then plug that t value in for the x equation.
    That is not in English, what you do is you solve for when the height is zero:

    y_o + (V_0\, t \sin(\theta) - \frac{1}{2} gt^2)=0

    for $$ t, this is a quadratic in $$ t and so has two roots, you need the positive one (which is what you have found).

    Here's my work

    y=(\frac{-g}{2})t^2 + (V_o sin\theta)t + y_o which is in (At^2 + Bt + C = 0) format.

    t=\frac{V_o sin\theta + \sqrt{(V_o sin\theta)^2 + 2gy_o}}{g}

    Subbed my values in and I got t=2.1348 s

    Plugged that value for t in the x equation and got 66.4194 ft. How does my equation look for finding t? If its right then I think I can assume my values for t and x are correct as well.
    The final answer is OK, but you give too many significant digits (only 5 are justified)

    CB
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  3. #3
    Member VitaX's Avatar
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    Just a typo. Meant to say set y equation equal to zero.
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