Math Is Fun Forum

The path of a projectile launched at a height of h feet above the horizontal ground at an angle, θ, with the horizontal can be modeled by the parametric eequations

         
                         x=(Vo cosθ)t and y=-16t² +(Vo sinθ)t + h,

where t is measured in seconds and Vo is the initial velocity of the projectile in feet per second. The centerfield wall in a ballpark is 14 feet in height and 420 feet from home plate. When a baseball player swings his bat at home plate, the bat makes contact with the ball 3 feet above the ground at angle θ ,with the  horizontal. Write a set of parametric equations that describes the path of the ball when it leaves the bat at a speed of 140 miles per hour.

Using your answer from the above exercise, determine the minimum value of  angle   θ , correct to the nearest tenth of a degree, for which the ball will go over the centerfield wall

Find the rectangular equation for this curve:

y=cos2t, y=sin2t; π≤t≤π