Four persons p q r s are initially at four corners of a square of side each person now moves with a constant velocity v in such a way that she always moves directly towards q
Answers
Answer:
what we have to do 8 in this question.
Complete Question: Four persons P, Q, R and S are initially at the four corners of a square of side 'd'. Each person now moves with a constant speed 'v' in such a way that P always moves directly towards Q, Q towards R, R towards S and S towards P. Find time after which these four people will meet.
Answer:
Time, t = d/v
Explanation:
[Refer to the attached image 1 to better understand the case]
Given;-
Length of Square side = d
Velocity of all persons = v
&, All person are moving in the direction as mentioned in the question.
Now;-
If we quite deeply observe the scenario, we will be able to have a brief idea whether the object will meet even and if they do, where will that exactly going to happen.
Guessing from the case, you may promptly opt that since every person is moving towards each of its target persons which in that case may sound that they will never meet together. But no, applying the concept of resultant vector in 2-D, we will be able to come out with a resultant v of every person which in turn will give a small square consecutively until they all reach the center and meet.
So, one thing is clear from the above discussion that they are going to meet. Now, we will find the time when they meet.
[Refer to attached image 2 for understanding this case]
Now, from the figure, it is quite evident that if we assume P to be at rest then Q gets an additional velocity opposite in the direction to that of P's velocity. Since, Q has two two velocities which are equal and perpendicular. Hence, from the below formula;
Speed = Distance/ Time, we obtain;-
Time = Distance/ speed [where, d= distance, v= speed, t= time]
t = d/v [ as d= d & v = v (given) ]
So, they will meet after d/v unit time.
Hope it helps! ;-))
