The cup on the 9th hole of a golf course is located dead center in the middle of

Question

The cup on the 9th hole of a golf course is located dead center in the middle of a circular green which is 40 feet in radius. Your ball is located as in the picture below. The ball follows a straight line path and exits the green at the right-most edge. Assume the ball travels 10 ft/sec. Introduce coordinates so that the cup is the origin of an xy-coordinate system. Provide numerical answers below with two decimal places of accuracy.

Thex-coordinate of the position where the ball enters the green will be.

(b) The ball will exit the green exactlyseconds after hitting the ball.

(c) Suppose thatLis a line tangent to the boundary of the golf green and parallel to the path of the ball. LetQbe the point where the line is tangent to the circle. Notice that there are two possible positions forQ. Find the possiblex-coordinates of Q:

smallestx-coordinate =
largestx-coordinate =

please provide some numbers with your solutions....Thanks

Explanation / Answer

A. To solve this, start off by writing down the two equations. y= mx + b is the first. Here, you have to plug in values you know to solve for b. x^2 + y^2 = 40^2 is the second equation of the circle. Once you have solved the first equation, plug it into the circle equation for y, and then simplify. In the end you will get something much like (something x^2 - something x - something) = 0. Use the quadratic formula and you will get your answer (make sure to choose the correct one). B. This is the easy question of the three. Simply use D=R*T (well and a^2 + b^2 =c^2). C. This is the tricky one. If you're in the same math I am, I'll assume that you haven't yet covered implicit differentiation (or differentiation at all for that matter). However, since this is the only way I could find how to solve it, I explain it to the best of my ability. Step One: Find the slope of the parallel line (you should already have this: see basic geometry) Step Two: Differentiate the equation of the circle Step Three: Plugin your slope into the y' to get an answer in the form of x = (something) * y. Step Four: Plug that X your original circle equation so you only have y. Step Five: Simplify Step Six: Enter your answer into web assign or homework.

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