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Math Help - Needing help figuring out this Vector Problem

  1. #1
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    Needing help figuring out this Vector Problem

    A football place kicker is about to attempt a field goal from the 30-yard line. He is lined up directly in front of the left goal post; but since there is a wind coming from the right side of the field, the kicker aims for the right goal post. This means that, from above, the ball will be kicked at a 79 angle to the 30-yard line.
    A.) The player kicks the ball at this angle with enough force to make the ball go 47 miles per hour, and the wind is blowing at 10 miles per hour. Use a vector sum of these two forces to show that, under these circumstances, the kicker will miss the field goal.

    B.) To make the field goal, the resultant force of the kick and the wind actually should have a magnitude of 50 miles per hour and a direction of 85. To counteract the 10-mph wind, with what speed--and at what direction--should the football player kick the ball?


    I am needing help figuring out the answers to this question. I would appreciate if someone could give great detail in explaining how to do this step by step to finding answers so I will know how to do it.
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  2. #2
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    Re: Needing help figuring out this Vector Problem

    This is, as you suggest, a "vector" problem. The problem, in the first problem, is to show that the ball will go "through the goal posts". If you set "x= 0" at the point where the kick starts, at the 30 yard line the goal post is at x= [and here, we have an problem. Is this "amateur football" or "professional football"? "Amateur football" (highschool, college) has the goal posts on the goal line, x= 30. But "professional football" has it 10 yards behind the goal line, x= 40]. Again, taking "z= 0" at the point where the kick starts, we need to have z, at the point the ball passes the goal post to be at least the height of the goal post. That is the same for both amateur and professional football but what is it? You will also need to find the width of the goal posts.

    Now, with all that, assume that the ball is kicked at an angle of [itex]\theta[/itex] degrees to the horizontal, as well as your given 79 degrees to the yard line. You can then calculate that the initial velocity vector is \left<47 sin(79)cos(\theta), 47 cos(79)cos(\theta), 47sin(\theta)\right>. Of course, the basic rule here is that the constant acceleration is that due to gravity [tex]\left<0, 0, -g\right>[tex] with g= -9.87 m/s^2. After t seconds, the velocity vector will be \left<47 sin(79)cos(\theta), 47 cos(79)sin(\theta), gt\right>+ \left<0, -10, 0\right> where that last vector is the wind velocity. Then, of course, you can find the position vector at each second, t, by integrating. However, I notice that this is posted under "preCalculus" and I don't know any way to do this without Calculus- unless you are given a formula for motion under at constant acceleration.
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  3. #3
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    Re: Needing help figuring out this Vector Problem

    It would be amateur football. This whole problem I found extremely confusing.
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