User:Parita 98/sandbox

 CALCULUS IN ANGRY BIRDS  

1.Description

To beat an angry bird level there are an infinite amount of equation for the path that a bird can take.

This would be far too difficult to calculate,so we are going to design a level based on the restriction of the equation you create.

2.Formulate the math

Angry bird is on (0,5),while the pig is at (8,2).Assume the bir flies in a projectile

f(x)=$$-x^2+4x+5$$

Find the "ANGRY POINT",which is defined as the point whose tangent will touch the pig's location.

3.Solve the Math

Here $$f(x)=-x^2+4x+5$$

If ,we want to find the cutting point of f(x) at X axis

$$f(x)=0$$

$$-x^2+4x+5=0$$

$$x=-1$$ or $$x=5$$

we have to take positive number so $$x=5$$ i.e.$$(5,0)$$

As we know that target is on tangent line,we have to write the tangent line function in tems of $$x_0$$

$$(x-x_o) f'(x_0)=y-y_0$$-(1)

Now,$$f(x)=-x^2+4x+5$$

$$f'(x)=-2x+4$$

$$f'(x_0)=-2x_0+4$$(2)

And $$y_0=-x_0^2+4x_0+5$$(3)

By Substtiting (2) and (3) in (1)

$$(8-x_0)(-2x_0+4)=2-(-x_0^2+4x_0+5)$$

By solving this equation w can get $$x_0=13.385$$ OR $$x_0=2.61$$

But we cannot take $$x_0=13.385$$,as it is greater than 5

So,We have to consider $$x_0=2.61$$

By putting $$x_0$$ in quation (3)

we get $$y_0=8.63$$

So,the Angry point is $$(2.61,8.63)$$

4.Application

This solution will be helpful while playing Angry birds.

This situation often occur in wars also.So we can calculate the point there also.

5.Bibliography

1.http://Quora.com//How-is-calculus-used-in-real-world

2. youtube.com