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homework2 - UNIVERSITY OF COLORADO AT BOULDER PHYS 2210...

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PHYS 2210 UNIVERSITY OF COLORADO AT BOULDER CLASSICAL MECHANICS AND MATH METHODS, SPRING, 2011 Homework 2 (Due Date: Start of class on Thurs. Jan 20 ) NOTE: Be sure to show your work and explain what you are doing. (Correct answers, for which we cannot follow the work, are worth no credit). 1. (4 pts) A particle is projected with velocity v 0 straight up a slope which makes an angle α with the horizontal. Find the time required to return to the starting point. (assume frictionless motion) Explicitly check the units of your final formula, and discuss the special cases α 0 and α 90 . 2. A soccer player kicks the ball with a velocity v 0 at an angle 45 (to reach maximum range). She want to kick it in such a way that it barely passes on top of two opposite team players of height h (12 pts: 4+4+4). (a) Show that if the separation between the two opponents is d v 0 g v 2 0 ? gh , the soccer player succeeds. (What is the numerical value of the ? in this formula?) (b) Use Mathematica to plot d as a function of v 0 , setting h = 2 m . Hint: If you want to plot a function f [ x ] vs x with x 0 < x < x 1 with Mathematica you can use the instruction Plot[ f [ x ] , { x, x 0 , x 1 } ] . Sqrt[] is the syntax for square roots. Note that Mathematica can’t plot a function with symbolic coe cients (so you have to plug in the values for both g and h
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