MATH 123 Calculus I
MATH 225 Calculus III
Dr. Ed Donley
Assignment 1
Due Wednesday, February 16, 2011
Instructions: Each group of three students should submit one typed report from the group. This report should be well-written, describing the problem, your group's solution, and any pertinent intermediate steps required to obtain that solution. Include mathematical equations and diagrams where relevant. Computations and graphs should be created on your calculator. Your report should include screen shots of graphs, where appropriate. Each of the three group members should be responsible for writing the report for one of the three assignments during the semester. The group member who writes this report should be different from the group members who write the reports for the other projects. List all group members' names and identify the primary writer on your report.
Suppose that a ball is rolled off of a 3-foot-high table at a speed of 2 feet per second. Further suppose that the ball rebounds from the floor at the same angle with which it hit the floor, but retains only 60% of its speed due to the energy absorbed by the floor on impact. You will probably need to use a combination of calculations, empirically based conjectures, and mathematical theory to solve the following problems.
a) Find the angle of impact when the ball first hits the floor. Find the angle of impact when the ball hits the floor the second, third, and fourth time.
b) Calculate the vertical distance that the ball travels after each of the first few bounces. Is there a pattern? If so, what is it?
c) How far does the ball travel vertically after each bounce (not just the first few bounces)?
d) How far does the ball travel horizontally after each bounce?
e) What is the total distance that the ball travels after each bounce?
f) Does the ball continue bouncing for all time? Explain.
g) Find the total horizontal distance traveled by the ball.
h) Find the total distance traveled by the ball.
i) Graph parametric equations on your calculator for the first three bounces. Include in your report the graph and the equations as you entered them into your calculator.
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