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Two persons p and q start from the points A and B respectively as shown in figure .P and Q have speeds v=12m/s in shown directions towards point O. When the distance between P and Q is 120m then Q increases its speed to 15 m/s . Then who will reach the point O first. A. P B. Q C. Both reaches simultaneously D. Data is insufficient Please give detailed solution. The ans is option A

Two persons p and q start from the points A and B respectively as shown in figure .P and Q have speeds v=12m/s in shown directions towards point O. When the distance between P and Q is 120m then Q increases its speed to 15 m/s . Then who will reach the point O first.
A. P
B. Q
C. Both reaches simultaneously
D. Data is insufficient
 
 
Please give detailed solution.
The ans is option A

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Grade:12

1 Answers

Himanshu Rathour
119 Points
5 years ago
OB=300
Let distance between p and q become 120 after t s. 
And are at point C and D. 
Now, because p and q are moving with equal speed hence, CDO will be a right angled triangle. 
Distance covered in time t by p and q=12t
CO=240-12t
DO=300-12t
(300-12t)²=(240-12t)²+(120)²
18000=1440t
t=12.5s
Therefore after 12.5 s p is at 240-12*(12.5)
=90m from 0
q is at 300-(12*12.5)
=150 form O
Now q speed of q has become 15m/s
Time taken by q to reach point O
=150/15
=10s
Time taken by p to reach point O
=90/12
=7.5s
Hence p will reach first at point O
 

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