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exam-1

# exam-1 - Physics 1A Practice Problem 3 1 Free Kick(30pts...

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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 . 8m 10m H = 2 . 44m 30m θ = 30 (a) If you usually like to kick the ball with an angle θ = 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 0 cos θ ) t - 1 2 gt 2 + ( v 0 sin θ ) 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 0 cos θ ) T - 1 2 gT 2 + ( v 0 sin θ ) T bracketrightbigg Notice that we have two unknowns ( T and v 0 ) 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 0 cos θ plugging into the second equation h , we get h = - 1 2 g D 2 w v 2 0 cos 2 θ + D w tan θ so that 1 2 g D 2 w v 2 0 cos 2 θ = D w tan θ - h or v 2 0 = 1 2 cos 2 θ g D 2 w D w tan θ - h = gD w 2 cos 2 θ 1 tan θ - h D w or v 0 = radicalBigg gD w 2 cos 2 θ 1 tan θ - h D w = 12 . 8 m s

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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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exam-1 - Physics 1A Practice Problem 3 1 Free Kick(30pts...

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