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# Tag Archives: vectors

## Displacement – A Numerical Problem

A fly is sitting in the middle of a wall of a cubic room of side ’a’.If it flies and sit to one of opposite corner of the wall. Find its displacement?

If the fly sit on the same wall on the horizontal, (from A to B in the diagram) the displacement is “a
If the fly sits on the diagonally opposite corner on the same wall, (from A to C in the diagram) the displacement is “√2 a
If the fly sits on the corner on the longest diagonal of the room,  (from A to H in the diagram) the displacement is “√3 a

## Tensor

streess is tensor,then,what is meant by tensor?

rupasri

Ans:

Tensors are used to represent the relation between vectors. They are geometrical objects which show’s    the  relation between vectors, vectors and scalars.It is  a geometrical maping of the relations .Tensor analysis ,a branch in mathematics is helping to solve the complex equations in which many vectors are involved

for further reference visit  http://www.grc.nasa.gov/WWW/k-12/Numbers/Math/documents/Tensors_TM2002211716.pdf

## Numerical from Kinematics and vectors

1. A jetliner moving at 500. km/h due east moves into a region where the wind is blowing from exactly NW toward the SE at a speed of 127 km/h. What is the new velocity of the airplane? you must include both magnitude and direction in your answer.
2. The speed of a train changes from36km/h to 72km/h in 10sec. calculate the distance travelled during this time

## Resolution of Vectors

From: Vakas

Subject: Resolution with geometry
Message Body:
Dear sir,
I m not able to understand that when we resolute mg in a inclined plane that plane having angle theta,how does the vertical component goes through inclined surface & cos comp opp to N.
explain with geometry so that i don’t get confused in future in determining the two comps is right direction.

Ans:

In a right angled triangle,

$cos\theta =\frac{adjacent side}{hypotenuse}$

and

$sin\theta =\frac{opposite side}{hypotenuse}$

When mg is resolved into mutually perpendicular directions, one parallel to plane and the other perpendicular to the plane (opposite to the Normal reaction), the component which is adjacent to θ is the cos component and the one away from θ is the sine component.

Students find difficulty ,mainly in identifying the angle .

See the diagram below and try to analyze

## Rain and Man problems – How to solve?

“How to solve rain and man problems from motion in one dimension?”

The problem is solved using principles of vector addition.

There is a simple logic to remember

A/C = A/B x B/C

If we represent diagrammatically (in the form of vectors) the velocity of rain wrt ground, velocity of man wrt ground and velocity of rain wrt man, then we can write

Vr/m = V r/g + Vg/m = V r/g – Vm/g = V r/g + (- Vm/g)

Where (- Vm/g) is the negative vector of Vg/m

I will be adding illustrations soon.

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