Challenge Activity (Parabolic Motion)

What happened:

A challenge activity that we did in class was set up with a diagonal ramp connected to a horizontal ramp that was set up on a table. Beside that table was a cup that the marble needed to land in. The goal of the challenge was to find out where to release the marble on the diagonal ramp so that it ultimately ends up landing into the cup. However, we were not allowed to test drop the marble at different places on the ramp to see where it would go. 

During the process, my group tried to calculate the acceleration of the marble going down the horizontal ramp and the time it takes. We did this by finding the mass of the marble, finding the angle degree of the diagonal ramp, and by test dropping the marble from the horizontal ramp (but catching the marble right when it got to the horizontal ramp) and timing it. Our group realized right when the marble gets onto the horizontal ramp, the velocity would become constant (because the marble in not moving at an angle). However, within the 45 minutes, our group was not able to complete the calculations and finish the challenge.

How I would redo the challenge:

Looking back, I would use the distance of the cup from the table and the height from the ground to the table surface to try to calculate at what rate the marble needs to be moving in parabolic motion to land in the cup. I would need to somehow find the rate at which the marble needs to be moving in parabolic motion to land in the cup. (How would I solve for this using quadratics? Can I solve this by using the kinematic equations too?) I can test drop the marble vertically from the height of the table and time how long it takes for the marble to travel and hit the ground. That would be how long it takes for the marble to travel when it falls from the ramp into the cup. Once I find that rate, I will know how fast the marble needs to be moving constantly on the horizontal ramp. Afterwards, I would then find the rate of acceleration of the marble going down the ramp. When I have that value, again, I would use a kinematic equation to see how much distance would need to be traveled to reach the velocity that I am looking for. The equation I would use is ∆x= [(Vf)^2-(Vo)^2]/2a. (This means the change in position equals final velocity squared minus initial velocity squared all divided by two times acceleration.) For the final velocity, it is the velocity that the marble needs to travel on the horizontal ramp and for the initial velocity, it would be zero since the initial velocity of the marble right when one let's it go is zero. For the acceleration, it would be found by a=Fnet/m. (This means acceleration equals the net force divided by the mass of the object, in this case it is the marble.) Once I have that distance, I would then know how far up to release the marble on the diagonal ramp for it to land in the cup.

Actually, looking at it again, I do not think the previous method will work. I do not know what angle the marble is at right when it lands into the cup to solve for the parabolic motion and I do not know how to find the rate the marble needs to be moving in parabolic motion to land in the cup. How should I tackle this challenge?

Reflection:

When I was doing the challenge, personally, it was a struggle trying to work together with the other students. Different people in the group wanted to solve the challenge in different ways. Although we decided to have some people do one method and the others try another method, we all still failed to solve the challenge. Throughout the process, there were different people on different pages in terms of understanding what was going on in the situation. For myself, while the other people were already getting started with the challenge, I was still sitting there trying to digest the information and trying to think about how to solve the challenge. Overall, although there was teamwork, it was not necessarily the strongest. For myself, I realized that I'm really the type of worker who needs time to think about a problem first before jumping in and trying to solve it. It was difficult for me to think while everyone else was already busy working. To solve this issue, I need to work on my communication skills. Next time, when I am at work, I will communicate with my classmates how I feel, ask for some time to think and ask for clarity on any confusion that I have.