Things you didn't know about GTA Vice City

12 years, That's a long time and this game is so old, But its one of the best game I have ever played. Here's a few things you might have missed while playing the game.

Ray Liotta did it for the money

That's right the 'Goodfellas' star didn't knew how big GTA  was otherwise he would have asked a bigger paycheck for the voice of Tommy Vercetti. Two of the missions "Cop Land" and "No Escape" are named from Ray Liottas movies with the same name.

GTA 3 radio

You can hear bits of radio from GTA 3 while seeking radio stations.

Rockstar Games logo

Its obvious that you can see rockstar games logo everywhere since they made it. Did you know 'There is a star constellation in the shape of eastern sky at night'. You can also increase the size of moon while shooting at it.

Drug references

There's hidden drug references from Jeremy Robard, a motivational speaker from the in game radio  VCPR.
His shows "Motivate,Demonstrate,then Motivate Again", " Think,Hold that thought,Complete" and"Learn,Start,Do" contains hidden references to drugs.  Abbreviation of these shows reads MDMA(Ecstasy), THC and LSD.

VC R29

Have you ever checked the license plate of vehicles in vice city?. They all reads the same!

Submarine

Yes, there's actually a submarine in vice city. Its useless, You cant access it since you die the moment you touches the water. It is situated near "North Point Mall". You can ride a working submarine in GTA5.

Unused Weapons

These weapons weren't lucky enough to be featured in the final version of the game. The textures can be found in PS2 discs. 

Did i miss something? Comment below and i will add it as soon as possibe

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Banking of roads, How to derive equation from a Banked road. Easy Physics

Banked Roads

When a vehicle goes around a curved road, It requires some centripetal force. If we raise the outer edge, a component of normal reaction of the road will contribute to the centripetal force in addition to the contribution of friction.This phenomenon of raising outer edge of the curved road is called banking of roads.

Deriving equation for banked roads

Since there is no acceleration in the vertical direction. The net force along this direction must be 0, hence

The centripetal force is provided by the horizontal components N and f

But(The law of static friction)

Substituting value of f in equation 1 and 2

From equation 4

Substituting this value in equation 5 gives,

v changes to vmax because we applied law of static friction.

Dividing each term of LHS by cosθ

Equating

We get

When friction is not needed.The equation becomes.

At this speed frictional force is not needed at all to provide the necessary centripetal force.

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How to do Mathematical Induction, Easy guide for beginners

What is mathematical induction?

It is a mathematical way to prove things by deductive reasoning.

An example for deductive reasoning

4 is divisible by 2
Any number divisible by two is an even number,therefore
4 is an even number. 

You should have got the idea by now.

Principle of mathematical induction

A popular example is a set of tiles placed near each other

The first tile falls,
If any tile falls its successor falls. 

Mathematical induction is very easy, Make sure you write each step and solve it by yourself.

How to solve Mathematical induction. 

Here is an example for Mathematical induction, The formula to find the sum of positive integers 1,2,3...n is given below.

We can prove the equation by giving different values for n.  But we cannot check the value for all integers.  We need something like a chain reaction for that.  If the value is true for a positive integer k, then (k+1) should also be true in the equation. 

Solving a Mathematical induction problem

Here's a pattern of numbers, note that:

The sum of first two odd natural numbers is the square of second natural number  sum of first three odd natural numbers is the square of third natural number, the pattern goes on

We need a formula for this patternz It is given below

To solve the Mathematical induction

Let us write P(n)

 

When putting the value of P(n)=1, we get 1 which is true.

Let P(k) be true 

Now assume P(k+1) is also true. Get the value for P(k+1) 

Change the value of P(k) from equation to P(k+1)

Look at the highlighted part its the same value as P(k)

We replace it with RHS value of P(k)

 

Equate the LHS, we get a Quadratic equation.  Solve it further, we get the same value 

Hence proved.

Another example of mathematical induction. 

For all n>=1 (Greater than or equal to), prove that

Step 1:

Let P(n) be

Step 2:

For n=1

Step 3:

Now, n=k

Step 4:

Now n=(k+1)

Step 5:

Replacing with value of P(k)

Step 6:

Equating

 we get the same value of RHS from Step 4.

That was so easy! Any questions? Comment below.

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