# parametric equations problem

• Apr 1st 2009, 08:05 PM
oblixps
parametric equations problem
The center field fence in a ballpark is 10 feet high and 400 feet from home plate. A baseball is hit at a point 3 feet above the ground. It leaves the bat at an angle of (theta) degrees with a horizantal at a speed of 100 miles per hour.

x = (v0 cos(theta))t and y = h + (v0 sin(theta))t - 16t^2
The initial velocity is v0 feet per second and the path of the projectile is modeled by the parametric equations. The projectile is launched at a height of "h" feet above the ground at an angle of (theta) with the horizantal.

a) write a set of parametric equations for the path of the baseball.
b) Use a graphing utility to graph the path of the baseball for theta = 15 degrees. Is the hit a home run?
c) Use a graphing utility to graph the path of the baseball for theta = 23 degrees. Is the hit a home run?
d) Find the minimum angle required for the hit to be a home run.

i got everything except for part d) please help me with part d). how do you find the minimum value of theta that you can hit a homerun with in this parametric equation?
• Apr 2nd 2009, 02:46 AM
HallsofIvy
Presumably, in doing (a), (b), and (c), you recognized that y(t) had to be at least 10 when x(t)= 400. That is, you solved the equation x(t)= 400 for t, put that into y(t) and showed that y was larger than 10. Do the same, leaving theta as a variable: t= 400/(v0cos(theta), so y= 3+ v0 sin(theta)(400/v0 cos(theta))- 16(400/v0cos(theta))^2= 10. Presumably you have already found v0 in feet per second so that is an equation for theta. Solve that equation.
• Apr 3rd 2009, 05:36 PM
oblixps
i got it now! thanks!