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Question about Invasion Sports

Physical Education

Originais Teachy

Invasion Sports

Hard

(Originais Teachy 2024) - Question Hard of Physical Education

During a soccer match, a player takes a penalty kick from a distance of 12.0 m from the center of the goalpost, which has a width of 7.32 m. Considering the kick as an oblique projectile motion and neglecting air effects, determine the initial velocity with which the ball must be kicked so that, after covering half of the distance to the goal, its height is 2.44 m, passing exactly at the point where the height of the crossbar begins. Additionally, assuming a crosswind speed of 5.0 m/s, determine the direction in degrees at the moment of the kick so that the ball, after overcoming the influence of the wind and without further deviations, reaches the intersection of the crossbar and the vertical bar of the goal. Consider the coordinates (0,0) at the penalty kick launch point.
a.
The initial velocity with which the ball must be kicked is approximately 6.93 m/s in the direction of 0° (relative to the x-axis).
b.
The initial velocity with which the ball must be kicked is approximately 4.91 m/s in the direction of 70.28° (relative to the x-axis).
c.
The initial velocity with which the ball must be kicked is approximately 9.81 m/s in the direction of 45° (relative to the x-axis).
d.
The initial velocity with which the ball must be kicked is approximately 2.44 m/s in the direction of -71.57° (relative to the x-axis).
e.
The initial velocity with which the ball must be kicked is approximately 6.93 m/s in the direction of -70.28° (relative to the x-axis).

Answer sheet:

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