| 1. After Mr. Zillmer got hit in the head with a pitch, Mr. Rukamp came up to bat. The equation h = -.004d2 + .96d + 3 represents the path the ball took after Mr. Rukamp hit the first pitch (h is the height of the ball, in feet, and d is the distance, in feet, the ball is from home plate). |
| a. How far off the ground was the ball when it was hit by the bat? |
| b. What is the height of the highest point that the ball reaches? (Round answer to the nearest tenth of a foot and show work) |
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c. How far (horizontally) from home plate is the ball at that moment? (Round answer to the nearest tenth of a foot and show work) |
| d. What was the (linear) distance between the point where the ball was hit and the "max" point? (Hint: You will use the Pythagorean Theorem) |
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e. Make a diagram of the situation above. Include all the values involved and the axes. |
| 2. Later in the game Mr. Zillmer came to the plate and he got hit in the head with a pitch again. This brought up Mr. Rukamp once more. The equation h = -.002d2 + .58d + 2 represents the path the ball took after Mr. Rukamp hit the first pitch (h is the height of the ball, in feet, and d is the horizontal distance, in feet, the ball is from home plate). |
| a. Assuming the baseball field was big enough and nobody caught the ball, how far from home plate would the ball land? (Show work) |
| b. Use trigonometry to estimate the angle (from the horizontal) that the ball was hit. (Show work) |
| c. Mr. Schumacher is playing the infield when the ball is hit toward him. If he can leap and catch a ball 11.5 feet high, how close to home plate does he need to be to be standing in order to reach the ball (if he’s crazy enough to be standing that close!) |
| d. If a ten-foot tall outfield fence was placed at a distance of 280 feet from home plate, would the hit be a home run? (Show work) |
| *By how many feet (to the nearest tenth of a foot) does the ball clear or fall short of clearing the fence? (Show work) |
| e. Make a diagram/picture of the situations above. Include all the values involved and the axes. |
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