Dynamic Calculus
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Fore!
This applet focuses on the importance of the first derivative in describing and sketching the graph of a function. By applying calculus to the equation of the flight path, determine the greatest height reached by the golf ball.
[You can reset the applet at any time by clicking the 'circular arrows' icon in the top right corner]
- In the game of golf, a 'hole-in-one' is scored when the player reaches the hole with only one 'shot'. By varying the position of the 'flag' and/or by varying the power of the golfer's swing, try to reach the flag with one shot. [Move the 'play shot' slider all the way to the right to play the shot. Move the slider all the way to the left to reset and play another shot. At the completion of each shot review the information provided and use this to adjust the position of the flag and/or the power of the golfer's swing.]
- After completing a shot, write down the equation of the flight path of the ball. Using calculus, determine the position of the stationary point. Check your answer by clicking the 'checkbox'.
- What conditions must exist for a stationary point to be classified as a maximum turning point? Show that the point in question (2) is a maximum turning point.
- What fraction of the ball's flight is completed when the maximum height is reached? What was the maximum height reached by the ball on the last shot?
- Given the position of the stationary point, adjust the power of the golfer's swing to achieve a hole-in-one on his next shot.