1. A ship sailing on the open sea leaves Port A for Port B at a bearing of N25oW. A wind of 6 km/h on a bearing of N10oE blows the ship off course. If the ship is capable of 35 km/h in still water, find the new speed and direction relative to the shore.

2. A boat is capable of 20 km/h in still water. You wish to cross the river to a point directly across from your present position. At what angle to the bank should you steer the boat if the current is 8 km/h?

3. A boat is capable of 20 km/h in still water. You wish to cross the river downstream so that the angle the boat's push makes with the bank is 50o. At what angle to the bank should the boat steer if the current is 8 km/h? How long will it take to cross if the river is 1.7 km wide?

4. A boat is capable of 20 km/h in still water. You wish to cross the river to a point 0.6 km upstream from your present position. If the current is 8 km/h and the river is 1.5 km wide, at what angle to the bank should you steer the boat? How long will it take you to cross?

5. An aircraft is currently on course flying from A to B, a distance of 400 km, on a bearing of S20oE at 350 km/h. A 50 km/h wind blowing S80oE starts to blow the aircraft off-course. At what new bearing should the pilot steer in order to stay on course? What will the new speed be after the course correction?

6. You wish to swim across a river that is 0.3 km wide to a point directly across from your present position. If you can swim at a constant speed of 4 km/h in still water and the current is 2.5 km/h, at what angle to the bank should you swim so that you end up directly across on the other side ( i.e. your actual path is 90o to the bank)? What is your speed relative to the bank?

7. Three coplanar forces of 10 N, 20 N and x N act on a body and maintain it in a state of equilibrium. The x force acts along the horizontal and the 10 N force at...

...each of the following vectors in terms of and
(a)
(b)
(c)
(Total 4 marks)
2. The vectors , are unit vectors along the x-axis and y-axis respectively.
The vectors = – + and = 3 + 5 are given.
(a) Find + 2 in terms of and .
A vector has the same direction as + 2 , and has a magnitude of 26.
(b) Find in terms of and .
(Total 4 marks)
3. The circle shown has centre O and radius 6....

...December 2011
Vectors
Math is everywhere. No matter which way you look at it, it’s there. It is especially present in science. Most people don’t notice it, they have to look closer to find out what it is really made of. A component in math that is very prominent in science is the vector. What is a vector? A vector is a geometric object that has both a magnitude and a direction. A good example of a vector is wind. 30 MPH...

...Mehran University College
Of Engineering & Technology,
Khairpur Mir’s
VECTOR GROUPS
ENGR. AHSANULLAH MEMON
LECTURER
DEPARTMENT OF ELECTRICAL ENGINEERING MUCET KHAIRPUR MIRS
ZIGZAG CONNECTION OF TRANSFORMER
The zigzag connection of tranformer is also called the
interconnected star connection.
This connection has some of the features of the Y and
the ∆ connections, combining the advantages of both.
The zigzag transformer contains six coils on three
cores.
Its...

...is a vector which represents the initial state of a system, then there is a matrix M such that the state of the system after one iteration is given by the vector M x0 . Thus we get a chain of state vectors: x0 , M x0 , M 2 x0 , . . . where the state of the system after n iterations is given by M n x0 . Such a chain is called a Markov chain and the matrix M is called a transition matrix. The state vectors can be of one of two types: an...

...Vector graphics is the use of geometrical primitives such as points, lines, curves, and shapes or polygon(s), which are all based on mathematical expressions, to represent images in computer graphics. "Vector", in this context, implies more than a straight line.
Vector graphics are based on images made up of vectors (also called paths, or strokes) which lead through locations called control points. Each of these points has a definite...

...Sciences
ECE / ICE / MexE Department
ECE 352 VECTOR ANALYSIS
DEL OPERATOR
GROUP 3 Andaya, Rizalyn Ramos, Maria Issa P.
∇
Del is a symbol used in mathematics, in particular, in vector calculus, as a vector differential operator, usually represented by the nabla symbol ∇. Del may denote the gradient (locally steepest slope), the divergence of a vector field, or the curl (rotation) of a vector field. The...

...1. Gradient of a scalar field function
Scalar Function:
Generally, What Is Scalar Function?
The Answer Is that a scalar function may be defined as A function of one or more variables whose range is one-dimensional, as compared to a vector function, whose range is three-dimensional (or, in general, -dimensional).
Scalar Field
When We Talk about Scalar Field, We Are Talking about the Scalar Function Being Applied to a Space (More like Euclenoid Space etc) or, a...

...{draw:frame}
{draw:frame}
I.INTRODUCTION
*II.*BASIC CONCEPT OF SVPWM
Space Vector Modulation treats the two level inverter of fig.1 as a single unit which can be driven to eight unique states that each state creates a corresponding voltage vector. An electric-motor control system, comprising:
*a two level voltage source inverter.
III.*IMPLE*MENTATION OF SPACE VECTOR PWM
For the three phase two-level PWM inverter as shown in Fig.1,...