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Unformatted text preview: Physics 1A, Practice Problem 3 April 21, 2010 1 Free Kick (30pts) You are charged with taking a free kick in the most important soccer game of the century. Your teammate has been fouled a distance D g = 30 m from the goal (see figure). In order to score a goal, you must clear a wall of opposing player who are lined up a horizontal distance of D w = 10 m from you. The height of the wall is h = 1 . 8 m, and the height of the goal is H = 2 . 44 m. h = 1 . 8 m 10 m H = 2 . 44 m 30 m = 30 (a) If you usually like to kick the ball with an angle = 30 with respect to the horizontal, with what initial speed must you kick the ball to barely clear the wall of players D w away? Since the ball is in constant acceleration, we have bracketleftbigg x ( t ) y ( t ) bracketrightbigg = bracketleftbigg ( v cos ) t- 1 2 gt 2 + ( v sin ) t bracketrightbigg the ball just clears the wall at some time T : bracketleftbigg D w h bracketrightbigg = bracketleftbigg x ( T ) y ( T ) bracketrightbigg = bracketleftbigg ( v cos ) T- 1 2 gT 2 + ( v sin ) T bracketrightbigg Notice that we have two unknowns ( T and v ) and two equations. The rest of the problem is simply math: no more physical information needs to be added. Even though this is a physics class (and not a math class), I will still outline the mathematics to solve this problem. Notice that T = D w v cos plugging into the second equation h , we get h =- 1 2 g D 2 w v 2 cos 2 + D w tan so that 1 2 g D 2 w v 2 cos 2 = D w tan - h or v 2 = 1 2 cos 2 g D 2 w D w tan - h = gD w 2 cos 2 1 tan - h D w or v = radicalBigg gD w 2 cos 2 1 tan - h D w = 12 . 8 m s Physics 1A, Practice Problem 3 2 (b) With what initial speed must the ball be kicked so that it not only clears the wall of players, but also reaches the goal at the minimum height of h = 2 . 1 m , just beyond the reach of the goalkeeper....
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This note was uploaded on 05/29/2011 for the course PHYS 1A taught by Professor Musumeci during the Summer '08 term at UCLA.
- Summer '08