Question

Two particles A and B of equal mass are projected simultaneously with speed 10m/s each as shown in figure. Find the co-ordinate of COM at t =10 s(take g =10m/s^2)​

Answer 1

The c, o, m will be (0,0) as y co-ordinate will be 0 and x co-ordinate have same magnitude with opposite sign :)

Answer 2

 

velocity of projection v = 10 m/sec

 

@ = 60 degrees

 

horizontal distance, d = 10 m

Vertical distance h = 5 m

 

For A

 

r1 = (v cos@) t i + [v sin@ – ½ g t^2] j

 

For B

 

r2 = [d – v cos@ t] i + [ – h + v sin@ – ½ g t^2] j

 

so

 

r1 – r2 = [2 v cos @ t – d] + h j

 

r = |r1 – r2 | = sqrt [(2 v cos @ t – d)^2 + h^2 ]

 

 

For r (min)  (parallel condition)

 

dr/dt = 0

 

we will get

 

t = d / 2v cos@

 

putting the values

 

t = 10 / (2 * 10 * cos60) = 1 sec

 

Hope it helps