The centerfield fence at Yankee stadium is 7 feet high and 408feet from home pla
ID: 3096005 • Letter: T
Question
The centerfield fence at Yankee stadium is 7 feet high and 408feet from home plate. A baseball is hit at a point three feet abovethe ground. It leaves the bat at an angle of x degrees withthe horizontal at a speed of 100 miles per hour.
Find the minimum angle required for the hit to be a homerun.
The centerfield fence at Yankee stadium is 7 feet high and 408feet from home plate. A baseball is hit at a point three feet abovethe ground. It leaves the bat at an angle of x degrees withthe horizontal at a speed of 100 miles per hour.
Find the minimum angle required for the hit to be a homerun.
Explanation / Answer
The "parametric" part of parametric equations is writing somethinglike y = x^2 in terms of another parameter, such as time so thatyou have y as a function of t and x as a function of t. Now thatthat's out of the way, I believe your homework problem is mostlysolved here: http://colalg.math.csusb.edu/~devel/prec… Scroll down to near the bottom of the page where it says"Projectiles". Watch your units, and remember that the startingpoint was three feet above the ground. I'll go a little further. Take a look at that page I linked andfollow along, please! Draw a picture of the path of the ball on the x and y coordinateaxes. This will help a lot as you try to solve the problem. Makesure to note that at the starting point (x = 0), the ball isalready three feet off the ground (y = 3). We'll start with x. We're given and angle and initial speed.Converting 100 mph to feet per second gives you 146.7 ft/s, so weget this: x = 146.7 cos(theta)t For y, we have our initial vertical velocity, which will be 146.7 sin(theta)t opposed by acceleration due to gravity, which is (-32.2t^2)/2 = 16.1t^2 and we started 3 feet off the ground, so our y equation looks likethis: y = 3 + 146.7sin(theta)t - 16.1t^2 At this point, I believe the homework problem is solved. I hopethis has helped you get a better understanding of the subject! (http://answers.yahoo.com/question/index?qid=20100404221535AAJ4HNs)
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