1. Two friends watch a jogger complete a 400 m lap around thetrack in 100 s. One

Question

1. Two friends watch a jogger complete a 400 m lap around thetrack in 100 s. One of the friends states, "The jogger's velocitywas 4 m/s during this lap." The second friend objects, saying, "No,the jogger's speed was 4 m/s" Who is correct? Justify youranswer. 2. A ball on a porche rolls 60 cm to the porche's edge, drops40 cm, continues rolling on the grass, and eventually stops 80 cmfrom the porche's edge. What is the magnitude of the ball's netdisplacement, in centimeters? Can someone please help me solve these twoproblems...step-by-step please. Thank you in advance. I reallyappreciate it. 1. Two friends watch a jogger complete a 400 m lap around thetrack in 100 s. One of the friends states, "The jogger's velocitywas 4 m/s during this lap." The second friend objects, saying, "No,the jogger's speed was 4 m/s" Who is correct? Justify youranswer. 2. A ball on a porche rolls 60 cm to the porche's edge, drops40 cm, continues rolling on the grass, and eventually stops 80 cmfrom the porche's edge. What is the magnitude of the ball's netdisplacement, in centimeters? Can someone please help me solve these twoproblems...step-by-step please. Thank you in advance. I reallyappreciate it.

Explanation / Answer

Let the initial and final angular velocities of the jogger bewo and w respectively.The angular acceleration of thejogger is and the angular displacement is thereforewe get w2 - wo2 =2 or = (w2 -wo2/2) w = (2/t),wo = 0 and = 2radians or = ((2/t)2 - 02/2 *2) = (/t2) t = 100 s or = (3.14/(100)2) = 3.14 * 10-4rad/s2 we know that w = wo + t or w = 0 + 3.14 * 10-4 * 100 = 3.14 *10-2 rad/s = * 10-2 rad/s The circumference of the track is S = 2r or 400 = 2r or r = (400/2) = (200/) The linear speed is v = r * w = (200/) * * 10-2 = 2m/s The jogger's speed is v = 2 m/s 2.The angle made by the ball from the porche's edge to thepoint where it stops is tan = (40/80) or = tan-1(40/80) = 26.5o Let the initial speed of the ball be u The ball drops from a height h given by h = (u2sin2/2g) or u = (2gh/sin2)1/2 or u = ((2gh)1/2/sin) -----------(1) or u = ((2gh)1/2/sin) -----------(1) g = 9.8 m/s2 and h = 40 cm = 40 * 10-2m The magnitude of the ball's displacement is v2 - u2 = 2gS or S = (v2 - u2/2g) v = 0 or S = -(u2/2g) ------------(2) from (1) and (2) S = (((2gh)1/2/sin)2/2g) =(h/sin2) The magnitude of the ball's net displacement is Snet = S + 60 = (h/sin2) +60

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