Question

PHYS 121 – Special Problem 1 Multiple Representations and Kinematics

Two children are playing a game where they run towards each other and see who can reach a toy that is somewhere between them. In the beginning, Charlie is 23.7 m away from the toy, running towards it at a speed of 0.770 m/s, and is speeding up. At the same time, Amy is 12.5 m away from the toy, is running towards it in the opposite direction as Charlie at a speed of 2.70 m/s, and is slowing down. Charlie is increasing his speed by 1.22 m/s every second and Amy is decreasing her speed by 0.25 m/s every second. Your primary goal is to find out who reaches the toy first.

a. Draw a detailed picture illustrating the physical situation described above. Include a coordinate system choice, labelled velocity and acceleration vectors, and labels for any objects, times, etc.

b. Somewhere on or near the picture make a detailed list for all the important quantities. Use extra subscripts C and A for Charlie and Amy (i.e., viC would be Charlie’s initial velocity, aA would be Amy’s acceleration).

c. Solve the problem in each of the following ways (any order is okay, but all three are required):

i. Algebraic Approach:

1. Present a formal algebraic solution: write down the kinematics equations and decide on a strategy for solving for your unknown(s). Solve the problem in symbolic form for your desired quantities (plug in the numbers as the final step).

2. Use the results of your algebraic solution to give an answer for who reaches the toy first.

ii. Graphical Approach:

1. Present a graphical interpretation of the problem to solve: Neatly draw three blank graphs on one piece of graphing paper so that the horizontal axes are all aligned (time axes), making your graphs as large as possible.

2. It is typically easier to start with the acceleration graph to find the velocity graph than the other way around. Start this one with an acceleration vs. time graph – draw the acceleration graph for each child on a single graph. Explain your choices in detail.

3. Use the acceleration graphs you created to make the velocity vs. time graphs for both children (on the same graph). You will need to consider the initial velocity information for each child. Explain your choices in detail.

4. Use the velocity graphs you created to make the positon vs. time graphs for both children (again, on the same graph). You will need to consider the initial position information for each child. Also draw a position vs. time graph for the toy on the same graph. Explain your choices in detail.

5. Use the position vs. time graph to determine who reaches the toy first.

iii. Computational Approach

1. Develop a method for solving the problem numerically using the help of some computer software or programming tool. Some examples include Graphical Analysis, Maple, Mathematica, MS Excel, Python, VPython, Visual Basic, Java, C++, and Geogebra. Let me know if you have any questions about these.

Answer 1