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(b) A daredevil is shot out of a cannon at speed v (m/s) and angle from horizontal. Use dimensional analysis to determine which of the following expressions could be correct for the range D (m) that the daredevil flies before hitting the ground. Recall that acceleration due to gravity, g, has units (m/s²). Show how you got to your answer. (i) D = 2v² cos 0 (ii) D 2v² = sin 0 9 (iii) D = 2g sin cos (iv) D=2vg(cos - sin 0) (c) You see online that a group of intrepid international scientists has finally figured out a precise expression for a boomerang's horizontal distance x(t) as a function of time, after being thrown from any launch angle 0, at any initial speed vo, from any height h above ground: x(t): h² vot cos 0 Consider the limiting behavior of vo, meaning consider its extreme values of 0 and infinity while holding other variables fixed. Based on this analysis, are these scientists (and/or the news sources) correct? Show how you got to your answer.

(b) A daredevil is shot out of a cannon at speed v (m/s) and angle from horizontal. Use dimensional analysis to determine which of the following expressions could be correct for the range D (m) that the daredevil flies before hitting the ground. Recall that acceleration due to gravity, g, has units (m/s²). Show how you got to your answer. (i) D = 2v² cos 0 (ii) D 2v² = sin 0 9 (iii) D = 2g sin cos (iv) D=2vg(cos - sin 0) (c) You see online that a group of intrepid international scientists has finally figured out a precise expression for a boomerang's horizontal distance x(t) as a function of time, after being thrown from any launch angle 0, at any initial speed vo, from any height h above ground: x(t): h² vot cos 0 Consider the limiting behavior of vo, meaning consider its extreme values of 0 and infinity while holding other variables fixed. Based on this analysis, are these scientists (and/or the news sources) correct? Show how you got to your answer.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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(b) A daredevil is shot out of a cannon at speed v (m/s) and angle from horizontal. Use dimensional analysis to determine which of the following expressions could be correct for the range D (m) that the daredevil flies before hitting the ground. Recall that acceleration due to gravity, g, has units (m/s²). Show how you got to your answer. (i) D = 2v² cos 0 (ii) D = 2v² sin 0 9 (c) You see online that a group of intrepid international scientists has finally figured out a precise expression for a boomerang's horizontal distance x(t) as a function of time, after being thrown from any launch angle 0, at any initial speed vo, from any height h above ground: (iii) D = 2g sin cos (iv) D = 2vg(cos - sin 0) h² vot cos 0 Consider the limiting behavior of vo, meaning consider its extreme values of 0 and infinity while holding other variables fixed. Based on this analysis, are these scientists (and/or the news sources) correct? Show how you got to your answer. x(t): =
Transcribed Image Text:(b) A daredevil is shot out of a cannon at speed v (m/s) and angle from horizontal. Use dimensional analysis to determine which of the following expressions could be correct for the range D (m) that the daredevil flies before hitting the ground. Recall that acceleration due to gravity, g, has units (m/s²). Show how you got to your answer. (i) D = 2v² cos 0 (ii) D = 2v² sin 0 9 (c) You see online that a group of intrepid international scientists has finally figured out a precise expression for a boomerang's horizontal distance x(t) as a function of time, after being thrown from any launch angle 0, at any initial speed vo, from any height h above ground: (iii) D = 2g sin cos (iv) D = 2vg(cos - sin 0) h² vot cos 0 Consider the limiting behavior of vo, meaning consider its extreme values of 0 and infinity while holding other variables fixed. Based on this analysis, are these scientists (and/or the news sources) correct? Show how you got to your answer. x(t): =
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