Combination Kinematics Problem - Quadratic Formula
About 3 weeks ago I posted here because I needed help for a bonus question. Though I was told that I would need to do this myself due to it being a bonus. The test for it passed and I obviously didn't get it. However, I'm curious as to how to solve it. I was told by a friend that the quadratic formula is involved in this. The thing is, I'm not exactly sure how to apply it to this question:
"A boy and a ball are at rest at the top of an incline. The ball rolls down the incline with an acceleration of 0.2m/s^2. Twelve seconds later the boy chases after the ball with an acceleration of 9.0m/s^2. The length the incline is 60m. Draw a diagram before solving the problem.
a. Will the boy catch the ball before the end of the incline? Hint "When are their displacements equal?"
What am I supposed to solve for? Is it the velocities of the boy and the ball?
b. What is the velocity of the boy when he catches the ball.
c. At what time does the boy catch the ball?"
I'm guessing that the kinematic equation will be involved. I think that I will have to rearrange this equation into the form and then solve using the quadratic formula. Though, what equations will I use to represent the displacement of the boy and the ball?