Question

11.
Two persons P and Q start from points A and B respectively as shown
in figure. P and Q have speed v = 12 m/s in shown directions towards
point when the distance between P and Q is 120m, then Q increases
s speed to 15 ms. Then find out who will reach the point O first.
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Answer 1

Answer:

Explanation:

Given, Distance of point A from O is 240m.

Hence, P has to cover a distance of 240m with a speed of 12 m/s.

 

Time taken by P to reach O = Distance/Speed

= 240/12 seconds

= 20 seconds.

 

If B takes lesser time, then B will reach O first.

 

Consider the Triangle OBX (name the adjacent side of OA = BX).

Here, cos 37 = 240/Hypo [Since cos \Theta = Base/Hypotenuse]

cos 37 = 4/5

 

So, 4/5 = 240/h

=>h = 60 x 5m = 300m

 

So, B has to cover a distance of 300 m to reach point O.

 

Intial distance between P and Q is 180m.

Q changes its speed to 15m/s when the distance between them is 120m.

So, when Q changes its speed, it has already travelled 60 m, and has to travel a remaining of 300 – 60 = 240m

 

Q covers first 60m at a speed of 12m/s.

So time taken = 60/12 = 5 seconds.

 

Q covers the next 240m at a speed of 15m/s.

So time taken = 240/15 = 16 seconds.

 

So, total time taken by Q to reach O = 5 + 16 = 21 seconds.