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Homework 18 - Solution for Long-answer Homework 18 Motion...

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Solution for Long-answer Homework 18 Motion in a Plane problems Solution to Long-answer Homework Problem 18.1() Problem: An airplane is travelling at 100 m s at a height of 200m , and drops a relief package to refugees below, but the parachute attached to the package fails to open. (a)How long does it take for the package to hit ground? (b)How far does the package travel horizontally before it lands? (c)What is the velocity of the package when it lands? Report a vector quantity. (d)What is the speed of the package? Solution to Part (a) The time it take the package to hit the ground depends only on its vertical motion, so the equation we need is y f = y i + v y,i t + 1 2 at 2 Taking y f = 0 , and y i = 200m , and since we know v y,i = 0 , we have Δ y = - 1 2 gt 2 t = radicalBigg - y g = radicalBigg - 2( - 200m) 9 . 81 m s 2 = 6 . 4s Grading Key: Part (a) 2 Points Solution to Part (b) Again, motion is separable into horizontal and vertical components, which are independant of each other, so Δ x = v x Δ t = parenleftBig 100 m s parenrightBig (6 . 4s) = 640m Grading Key: Part (b) 2 Points Solution to Part (c) The y -component of the velocity is v y = v y,i + at = 0 - gt = - 63 m s The x -component has not changed, so vectorv = 100 m s ˆ x - 63 m s ˆ y There are other ways to report this vector, but this is the easiest, and is certainly adequate. Grading Key: Part (c) 2 Points Solution to Part (d) 1
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The speed is simply the magnitude of the velocity (reported in the last part) so v = | vectorv | = radicalBig v 2 x + v 2 y = radicalbigg parenleftBig 100 m s parenrightBig 2 + parenleftBig - 63 m s parenrightBig 2 = 118 m s Grading Key: Part (d) 1 Points Total Points for Problem: 7 Points Solution to Long-answer Homework Problem 18.2() Problem: You and your friend are playing racketball at the HPER. You are standing 7m from the wall, and you hit the ball towards it at a 30 angle above the horizontal, with a speed of 15m / s . The ball leaves the racket at a height of 1 . 5m .
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