Field Goal Projectile Problem: Time to Score!

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The kicker launches the ball with an initial velocity of 27.0 m/s at a 30.0° angle. Using trigonometry, the horizontal component of the velocity is approximately 23.1 m/s, while the vertical component is about 13.5 m/s. The horizontal distance to the goal posts is 35 m, which can be calculated using the formula d = vt, yielding a time of approximately 1.52 seconds to reach the posts. For vertical motion, the height can be determined using the formula for accelerated motion, factoring in gravity. The ball's trajectory can be analyzed further to confirm if it clears the 4.0 m height of the goal posts.
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A place kicker attempts a field goal, giving the ball an initial velocity of 27.0 m/s at an angle of 30.0° with the level field. The uprights are 35 m from the point at which the ball is kicked and the horizontal bar is 4.0 m from the ground.
At what time after the kick will the ball pass the goal posts?
 
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Start with the initial velocity. Use trigonometry to find the vertical and horizontal components. The horizontal part is motion at constant speed, d = vt. The vertical motion is accelerated and you can use the velocity and distance formulas for that motion. Go as far as you can and you'll be eligible for more help!
 

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