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Math Help - Parametric equations

  1. #1
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    Parametric equations

    Consider a projectile launched at a height h feet above the ground and at an angle θ to the horizontal. If the initial velocity vo feet per second, the path of the projectile is modled by the parametric equations:
    x= (vo*cosθ)t and y=h+(vo*sinθ)t-16t^2

    The center field fence in a ballpark is 10ft high and 400 ft away from home plate. The ball is hit 3 feet above the ground. It leaves the bat at an angle of θ degrees with the horizontal speed of 100 miles per hour.

    A) write a set of parametric equations for the path of the ball.
    B) graph the path of the ball when θ = 15 Is the hit a home run?
    C) find the minimum angle at which the ball must leave the bat in order for the hit to be a home run.



    I have no idea where to start.
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  2. #2
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    Quote Originally Posted by jazz20 View Post
    Consider a projectile launched at a height h feet above the ground and at an angle θ to the horizontal. If the initial velocity vo feet per second, the path of the projectile is modled by the parametric equations:
    x= (vo*cosθ)t and y=h+(vo*sinθ)t-16t^2

    The center field fence in a ballpark is 10ft high and 400 ft away from home plate. The ball is hit 3 feet above the ground. It leaves the bat at an angle of θ degrees with the horizontal speed of 100 miles per hour.

    A) write a set of parametric equations for the path of the ball.
    B) graph the path of the ball when θ = 15 Is the hit a home run?
    C) find the minimum angle at which the ball must leave the bat in order for the hit to be a home run.
    part (a)

    start by converting 100 mph into ft/s to get v_0 in correct units

    ... sub in your known values

    x = v_0 \cos{\theta} \cdot t

    y = 3 + v_0 \sin{\theta} \cdot t - 16t^2

    (b) do what it says ... graph the parametric equations in your calculator. since the fence is 400 ft away in the x-direction, solve the equation for t

    400 = v_0 \sin(15) \cdot t

    then use that value of t to find the y-position ... if it's greater than 10 ft, homerun.

    (c) here's where you can use your graphing calculator to play with the angle to ATQ.
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