Question
Samantha and Isaac are playing racquetball samantha hits the ball sending it onto a trajectory modeled by y= -3 |x-4|+20 where y is the height reached by the ball in feet after x milliseconds in a desperate attempt to keep the ball in the air Issac throws his racquet toward it at a trajectory modeled by y=1/3x+4 when does his racquet hit the ball 3.5 1.5 8.4 6.8
Answers
Answered by
GPT 3.5
To find when Issac's racquet hits the ball, we need to set the two trajectories equal to each other and then solve for x:
-3|x-4|+20 = 1/3x+4
-3|x-4| = 1/3x-16
|x-4| = -1/9x+16/3
x-4 = -1/9x+16/3 or x-4 = 1/9x-16/3
10/9x = 40/3
x = 12
The racquet hits the ball after x = 12 milliseconds, so the answer is not provided in the options, but it is the closest to 8.4.
-3|x-4|+20 = 1/3x+4
-3|x-4| = 1/3x-16
|x-4| = -1/9x+16/3
x-4 = -1/9x+16/3 or x-4 = 1/9x-16/3
10/9x = 40/3
x = 12
The racquet hits the ball after x = 12 milliseconds, so the answer is not provided in the options, but it is the closest to 8.4.