Need help with this Vector problem!

[marlim14]

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.


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 79º 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 85º. To counteract the 10-mph wind, with what speed--and at what direction--should the football player kick the ball?

 

[srmichael]

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.


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 79º 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 85º. To counteract the 10-mph wind, with what speed--and at what direction--should the football player kick the ball?

What have you tried so far?

I'll give you a hint: use <47cos79º,47sin79º> for the ball vector and <10cos180º,10sin180º> for the wind vector.

 

[marlim14]

What have you tried so far?

I'll give you a hint: use <47cos79º,47sin79º> for the ball vector and <10cos180º,10sin180º> for the wind vector.

Where did you get 180º from? Im so lost with this problem, I don't even know where to begin.

 

[srmichael]

Where did you get 180º from? Im so lost with this problem, I don't even know where to begin.

The wind is coming from the right side of the field so if you envision this on an coordinate system where the positive x-axis is East (directional angle of 0º), positive y is North (90º), negative x is West (180º) and negative y is South (270º), "coming from the right" is equivalent to heading West which is 180º.

Did your teacher show you how all vectors can be represented by the component form <m*CosΘ,m*sinΘ> where "m" stands for the magnitude of the vector and Θ is the directional angle of the vector? Then, if you have two vectors, you add these two component forms up for each vector and that new component form represents the resultant vector.

 

[srmichael]

Marlim14:

Ball Vector: <47cos79º,47sin79º> = <8.97,46.14>
Wind Vector: <10cos180º,10sin180º> = <-10,0>

Add these two vectors and you get the resultant vector of <-1.03,46.14>

So now you have to ask yourself, how would I know if he misses the field goal? There are 3 options here:

1) He does not kick it long enough.
2) He kicks it at an angle that would not put it through the uprights (i.e. he kicks it wide left or wide right)
3) It is blocked.

We can rule out the 3rd option . But with the resultant vector we can calculate the magnitude and the direction of the vector. Assuming the ball travels the needed distance (> 40 yards), which I assume they expect you to assume, we can calculate the direction the ball travels to determine if the kick is good. It states that he is kicking the ball directly in front of the left goal post. The left goal post is directly north of where the kicker is, which is a 90º angle from where he is. Thus, the direction of the resultant vector would have to be less than 90º (in the first quadrant if you envision a coordinate system), but not too much less than 90º to where he kicks it wide right, in order for the ball to be good. Since the x-value component of the resultant vector is negative with the y-value being positive, we know the resultant vector is in the second quadrant which is equivalent to the kicker kicking it wide left of the post and missing the kick.

Let's see waht you can do on Part B.