Biomechanics problem w/ vectors

[in10sivkid]

Hi everyone...I am in my last semester of college and physics has returned to my life.. It has been approximately 3 yrs since physics and 6 years since calculus so I am really rusty regarding classical physics (mechanics).

here is my problem

Listed below are three vectors that point from the origin of a right-handed orthogonal three-dimensional reference frame to the shoulder (V1 ), elbow (V2 ) and wrist (V3 ), respectively, of the throwing arm of a baseball pitcher. Note, i and j are unit vectors in the horizontal directions (j points towards home plate and i is perpendicular to j and points towards third base), and k is a unit vector pointing in the vertical direction.

V1 = (10.02 i + 11.08 j + 1.10 k ) m - Shoulder

V2 = (10.19 i + 11.33 j + 1.22 k ) m - Elbow

V3 = (10.27 i + 11.55 j + 1.36 k ) m - Wrist

I have to find a vector that points from the elbow to the wrist, the length of the forearm from the elbow to the wrist, and also the elbow angle in degrees. I am going to write out my thought process so hopefully you can correct me if I'm wrong. I believe I have to do vector subtraction in order to find this vector. I would take the V3 (wrist) - V2(elbow). I would align the tail of V2 on the tip of V3 in the negative direction and find the resulting vector.
for the i unit vector it would be 10.27 - 10.19 = .09
for the j = 11.55 - 11.33 = .22
for the k = 1.36 - 1.22 = .14

I have a vector that is .09i + .22j .14k

and I would find the magnitude to find the length of the forearm which would be the square root of (.09i^2 + .22j^j + .14^2)
= .276 m which sounds reasonable

then for the last part solving the angle of the elbow I am stumped.

any feedback/help would be amazingly appreciative.

thanks everyone!

 

[sarujin]

Everything looks fine so far (except that the final vector should be .08i etc if the numbers are correct).

For the elbow angle: did they specify which frame the elbow is measured against? If it is the angle between say the shoulder and wrist, where the angle would be 180 degrees if your arm is extended, then you must find the vector pointing from the elbow to the shoulder, then use the definition of the dot product to find the angle between (hopefully you've covered it).

 

[andrevdh]

Use the dot or scalar product to determine the angle. That is you need to define the vector pointing from the shoulder to the elbow. The scalar product of this vector and the one from the elbow to the wrist will be equal to the product of their magnitudes (the two vectors) and the cosine of the angle between them (the required angle).