Vector Problems - North Hunterdon-Voorhees Regional High .
Vector Problems
General Information Vectors act independently Example: A boat with a velocity of 20 m/s eastand a 7 m/s current flowing south.– The boat travels 20 m east every second– The river flows south 7 m each second– If the boat were not going east it would be carriedby the current in the same way it gets carried bythe current when it is drifting
Vector Addition Reminders Vectors are drawn as arrows Always combine vectors tail to head You can move a vector so long as you don’tchange its magnitude or direction The resultant is drawn from the tail of the firstvector to the head of the last vector The angle you are looking at is the angleformed by the tail of the first vector and thetail of the resultant
Vector Mathematics Always draw a diagram Use the Pythagorean Theorem for the magnitude ofthe resultant Use tangent for the size of the angle Make sure you accurately describe the exactdirection of the resultant Resultants have two parts– Magnitude with unit– Angle with reference degree
1. A boat travels west at a speed of 24 m/s across a river that isflowing south at 9 m/s. What is the resultant velocity of the boat?
Vector Diagram
Magnitude Calculationc 24 9 576 81 657 25.622
Angle Calculationtan 19 0.375 20.6 24
Final Answer25.6 m/s @ 249.4
2. A plane flies south at 650 mph with a cross wind towards the east at 130 mph. Whatis the resultant velocity of the plane?
Vector Diagram
Magnitude Calculationc 6502 1302 422500 16900 439400 663
Angle Calculationtan 1130 0.2 11.3 650
Final Answer662.9 mph @ 169
3. An airplane flying east at 310 m/s has a 45 m/stailwind. What is the resultant velocity of the plane?
Vector Diagram
Magnitude Calculationc 310 45 355
Angle CalculationEverything is headed east
Final Answer355 m/s @ 90
4. The Antarctic expedition drives their snowmobiles 185 milessouth from their camp. Then they turn and drive 70 miles west.Now it is time to return to camp. In what direction must theydrive and will they make it on 190 miles worth of gas?
Vector Diagram Note that this is aspecial case where theresultant vector appearsto point backwards. This is because that isthe path they will needto take back to theirbase.
Magnitude Calculationc 1852 702 34225 4900 39125 198
Angle Calculationtan 1185 2.64 69.3 70
Final Answer20.8 & No, they will have to walk 8 miles
5. Tarzan is swimming east at 2.4 m/s across a riverthat is 1660 meters wide and flows north at 5.2 m/s.
Vector Diagram
Magnitude Calculationc 2.4 5.2 5.76 27.04 32.8 5.7322
Angle Calculationtan 15.2 2.17 65.2 2.4
Final Answer5.73 m/s @ 24.8
B. How long will it take him to cross the river? Data Equation Math Answer d 1660 mva 2.4 m/s t d va t 1660 2.4 t 692 s
C. How far downstream will he end up? Data Equation Math Answer t 692 sva 5.2 m/s d va t d 692 5.2 d 3600 m(or about 2.5 miles)
4. The Antarctic expedition drives their snowmobiles 185 miles south from their camp. Then they turn and drive 70 miles west. Now it is time to return to camp. In what direction must they drive and will they make it on 190 miles worth of gas? Vector D
Why Vector processors Basic Vector Architecture Vector Execution time Vector load - store units and Vector memory systems Vector length - VLR Vector stride Enhancing Vector performance Measuring Vector performance SSE Instruction set and Applications A case study - Intel Larrabee vector processor
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12 VECTOR GEOMETRY 12.1 VectorsinthePlane Preliminary Questions 1. Answer true or false. Every nonzero vector is: (a) equivalent to a vector based at the origin. (b) equivalent to a unit vector based at the origin. (c) parallel to a vector based at the origin. (d) parallel to a unit vector based at the origin. solution (a) This statement is true. Translating the vector so that it is based on .
Vector Length (MVL) VEC-1 Typical MVL 64 (Cray) Add vector Typical MVL 64-128 Range 64-4996 (Vector-vector instruction shown) Vector processing exploits data parallelism by performing the same computation on linear arrays of numbers "vectors" using one instruction. The maximum number of elements in a vector supported by a vector ISA is
Unit vectors A unit vector is any vector with unit length. When we want to indicate that a vector is a unit vector we put a hat (circum ex) above it, e.g., u. The special vectors i, j and k are unit vectors. Since vectors can be scaled, any vector can be rescaled b to be a unit vector. Example: Find a unit vector that is parallel to h3;4i. 1 3 4
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anatomi tulang berdasarkan gambar berikut ini! Diaphysis: This is the long central shaft Epiphysis: Forms the larger rounded ends of long bones Metaphysis: Area betweent the diaphysis and epiphysis at both ends of the bone Epiphyseal Plates: Plates of cartilage, also known as growth plates which allow the long bones to grow in length during childhood. Once we stop growing, between 18 and 25 .
