IE IRODOV'S General Physics - Question 1

1. A motorboat going Downstream overcame a raft at a point A ;  T= 60 min later it turned back and after sometime passed the raft at a distance l = 6.0 km  from the point A. Find the velocity,assuming the duty of the engine to be constant.

Answer : Upstream - Downstream motion has to be calculated as per Time.

Unlike Distance based calculations which are two-dimensional ,Time based calculations are made as three-dimensional which includes the direction vector as well

At first, Dimensional Analysis is done to find out the equation strategy. This has been called dimensional analysis of vector equations . This is done as follows:

Since distance based calculation is involved ,   

distance / time = velocity ,which is a vector 

Hence [VT] = a constant (distance)

Hence the length between ' B' and 'P' in the figure ,which is 'BC' has to be found out . 

3-Dimensional approach to this 2-d problem is drawn below

Time at B = Time at P ( for raft (wooden log) and boat respectively)

Time = Distance / Velocity ; 

Therefore,  (l-BC)/Velocity raft  =  AP / Velocity P = 60 min

That means, (6 - BC )/V raft = 60 minutes = 1hour

V raft = (6 - BC) / 1

   As per modern trigonometry,                                                             

 ( Hypotnuese - square ) =( Base - square) + ( Altitude -square)

As per modern Trigonometry, Hypotnuese is 2 times bigger than altitude and base for unity triangle ( which is 1 mm in base )

Now, Indian Mathematics suggests ,PASCAL'S TRIANGLE for solving Trigonometry problems that are unknown to calculation.

In this Triangle, there are fifteen numerals altogether till the fifth degree as shown above. This shows that Indian Approach is based on intense mathematical calculation using a repetitive algorithm ,which is used in modern day, Computer program 

Here ,1 + 4 = 5 , but 6 is given ,Hence, we are showing it as given above in Pascals image .

Now if you calculate diagonally, these numbers can introduce you to Trigonometry ,which is as shown below

                      1  4  5  9  5       , which is known as Pascal's rule in trigonometry.  ( Inclined indicates triangular formation using number digits.)

So,  1 (square ) + 4 ( square ) = square root ( 17) which indicates that square has to be used diagonally in the Pascal's format shown above.

So , 1   2  √3  in triangle calculation becomes 1  2  3 as shown in Pascal's Triangle above ( diagonally)

So, Above BC becomes 3 ( And that is the Solution )