(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider a projectile launched at a height of h feet above the ground at an angle θ with the horizontal. If the initial velocity is v_{0 feet per second, the path of the projectile is modled by the parametric equations x=(v0cos θ)t and y=h + (v0 sin θ)t-16t2. The center-field fence in a ballpark is 10 feet high and 400 feet from home plate. The baseball is hit 4 feet above the ground. It leaves the bat at an angle of θ degrees with the horizontal at a speed of 100 miles per hour. Find the minimum angle required for the hit to be a home run 2. Relevant equations 3. The attempt at a solution So your basic equations are [tex]x=(146.67\cos\theta)t[/tex] [tex]y=3+(146.67\sin\theta)t-16t^2[/tex] by the question when x=400, y>10 the ball will pass over the fence so if I solve for the angle θ when x=400 and y=10 the angle I get should be the minimum passable. [tex]400=(146.67\cos\theta)t[/tex] [tex]10=3+(146.67\sin\theta)t-16t^2[/tex] [tex]\frac{400}{146.67\cos\theta}=t[/tex] sub that into the other equation [tex]y=3+(146.67\sin\theta)(\frac{400}{146.67\cos\theta})-16(\frac{400}{146.67\cos\theta})^2[/tex] I can get a common denominator and get it to [tex]7=400(146.67)^2\cos^2\theta\sin\theta-16(400)^2\cos\theta[/tex] but I'm not quite sure what to do after here to solve for θ.}

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# Homework Help: Parametric Equations Word Problem

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