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A question from kinematics – motion in one dimension

Natasha Sehgal Asked:

“A stone is thrown in a vertically upward direction with a velocity of 5m/s. If the acceleration of the stone during its motion is 10m/s^2 in the downward direction , what will be the height attained by the stone and how much time will it take to reach there?”

Answer:

Take,

u=5m/s

a= -10 m/s2

v=0 at the topmost position

S= Hmax = ?

The eqn of motion to use
v2 – u2 = 2aS
Which gives H = 1.25 m
From the eqn
v=u + at
t= 0.5 s

Limitations of Dimensional Analysis

Ashmeeta Bhattarai asked:

“What are limitations of principle of homogeneity of dimensional analysis?”

The dimensional analysis has the following limitations

  1. It fails while using it to derive a relation among physical quantities, if there are more than 3 unknown variables on which a given physical quantity depends
  2. It does not tell whether a given Physical quantity is a scalar or a vector.
  3. It does not tell us the value of constants involved
  4. It does not always tell us the exact FORM of a relation
  5. It cannot be used for deriving logarithmic, trigonometric or exponential relations
  6. A dimensionally correct equation may not always be the correct relation. (Because there are more than one physical quantity having the same dimensions)

Know some more? Write them as comments to this post

Rain and Man problems – How to solve?

Shashank Asked:

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

Answer:

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.

Principle of Homogenity of Dimensions

Binay Sharma asked:

“Explain the applications of the Principle of homogenity of Dimensions and its importance”

Principle of homogenity of dimensions states that “For an equation to be dimansionally correct, the dimensions of each term on LHS must be equal to the dimensions of each term on RHS.”

Applications

1. To determine the dimensions of an unknown quantity in an equation

2. To check the accuracy of an equation

3. To derive a formula connecting the given (or assumed) physical quantities

4. To convert a physical quantity from one system of unit to other

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