Question

While playing mini golf, you hit the ball off of a wall to attempt at making it in the hole. The ball is located at (5,4) and the hole is located at (9,8). The point where the ball hits the wall is (7,0). Write an equation for the path of the ball and then determine if you will make your putt.

Answer 1

if x<7 -> f(x)=4|x-7|

if x>=7 -> f(x)=2|x-7|

Explanation:

the general form of the absolute value function is f(x)=a|x-h|+k, where the vertex is (h,k).

so therefore h=7, and k=0.

the formula: f(X)=a|x-7| (if x is more than or equal to 7, less than 7 will be a negative equation.)

solve the equation for the ball moving from (7,0) to (9,8): f(9)=a|9-7|=8

8=2a

hence, a=4 if x>=7

solve for the ball moving from (5,4) to (7,0)

f(5)=a|5-7|=4

4=2a

a=2 if x<7

write the equation:

if x<7 -> f(x)=4|x-7|

if x>=7 -> f(x)=2|x-7|

whether I could make my putt depends on the player's skills, but there are also many variables to think of,

so I think it is less likely I would make my putt.

Answer 2

Drawing this out shows the angle the ball hits the wall is arcTan(4/2) = 63 degrees. It bounds upwards at and angle of arcTan(9/2) = 77 degrees, so the angle of incidence is not equal to the angle of 'bounce' unless some spin is put on the ball indicating a very good putter.....