Physics 123 Quizes and Examinations Spring 2007 Porter Johnson ...
Physics 123 Quizes and Examinations Spring 2007 Porter Johnson ...
Physics 123 Quizes and Examinations Spring 2007 Porter Johnson ...
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4. PHYS <strong>123</strong> - 052 QUIZ 2 15 February <strong>2007</strong>A long jumper leaves (level) ground at a speed of v 0 = 10 meters per second.• What is the maximum distance D that the jumper will travel beforereturning to the ground?• Under those conditions, determine the time of flight T <strong>and</strong> the maximumheight H reached by the jumper.Note: you may treat the jumper as a “point mass”, <strong>and</strong> take g = 10m/s 2 .Solution:Let the launch angle by θ. The horizontal <strong>and</strong> vertical components of velocityare, respectively,v 0xv 0y= v 0 cosθ= v 0 sinθIf the jumper takes off at time t = 0 from positions x = 0 <strong>and</strong> y = 0, thepositions at time t arexy= v 0 cosθt= v 0 sinθt − 1 2 gt2The time T at which the jumper returns to the ground is obtained by settingy(T) = 0, so thatv 0 sinθT = 1 2 gT 22v 0 sinθgThe distance traveled, D, is given by= TD = v 0x T = v2 0g (2sinθ cosθ) = v2 0g sin2θ
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