Assignment #2 (35 pts)
Name: ___________________________
1. Consider two general velocity vectors,
u1  u1iˆ  v1 ˆj  w1kˆ
(1)
u2  u2iˆ  v2 ˆj  w2kˆ
a. (4 pts) Find the dot product of u1 and u2 .
b. (4 pts) Find the cross product of u1 and u2 .
c. (4 pts) If the vectors are expressed as follows,
u1  4 y
v1  3 x
w1  0
u2  3 x
and
v2  4 y
w2  z
Evaluate the dot product and cross products of u1 and u2 that you found in parts a and b.
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d. (4 pts) If an ocean parcel is moving due southeast at 10 kts (meaning it is moving from NW
to SE), write its velocity vector using standard iˆ and ĵ notation.
2. The triple cross product identity is expressed as

    
A B  C  B A C  C A B
(4)
When dealing with rotating frames, such as the earth, the following term comes up when
calculating the acceleration:

 

where  is the angular rotation with units of s 1 and  is a position vector from the center to
the surface of the earth with units of m. This term,      , is called centripetal acceleration,
and we will see it again in Chapter 9.




a. (3 pts) Use the triple cross product identity on      :


b. (3 pts) What are the units of the expression      ?
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c. (3 pts) Without loss of generality, we can assume that
 xiˆ  yjˆ  zkˆ and that the rotation
axis is in the k̂ direction so   k̂ . Use this information to evaluate the expression you found
in question 2a.
3. More dot and cross-products.
a) (5 pts) Find the result of A  B if the coplanar angle between two non-zero vectors, A and
B , is 180°.
b) (5 pts) Find the result of A  B if the coplanar angle between two non-zero vectors, A and
B , is 180°.
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