00:01
Hello students, here renee is walking 3 km east of the cottage.
00:05
So, let us consider c be the cottage.
00:07
From c to q she travels 3 km and let us consider a be the island and from q to a she travels 2 km and she can start to swim at any point p between the cottage and the point q.
00:20
So, let us consider the distance between the point p and q is x, then c to p will be 3 minus x.
00:28
Here we have to find the minimum possible time for renee to reach the island if she walks at a rate of 3 km per hour and swims at a rate of 2 km per hour and first we have to find the distance between p, a.
00:45
Therefore, we can say that the distance from the distance to reach a from p is which is given by the pythagoras theorem.
01:04
Therefore, we will get p, a equal to root of x square plus 4.
01:09
Then from the diagram we can say that it is root of x square plus 4 and we have to find the time.
01:21
Therefore, the time taken by renee to travel c, p is from the diagram we can say that the total time is the time taken from c to p plus time taken from p to e.
01:48
So, first the time taken from c, p is let us consider the time as t1 which is equal to 3 minus x by here she travels at a rate of 3 km per hour by walk.
02:03
Therefore, it is 3 and the time taken to travel e, p is t2 equals to root of x square plus 4 by 2 where she swims at a rate of 2 km per hour and the total time will be t1 plus t2.
02:39
Here t1 is 3 minus x by 3 plus t2 is root of x square plus 4 by 2 which is the total time.
02:48
Here we have to find the minimum time such that we have to find d square by dt d square t by dt square.
02:55
Here we are differentiating with respect to x.
02:59
Therefore, we have to find d square t by dx square...