Two bodies of mass 4 kg and 5 kg are moving along east and north direction with velocities 5 m / s and 3 m / s respectively . Magnitude of velocity of centre of mass of system is . . . . . . . . . : -

1 ) Two bodies of mass 4 kg and 5 kg are moving along east and north direction with velocities 5  m / s and 3 m / s respectively .  Magnitude of velocity of center of mass of system is . . . . . . . . . : -

A ) 20 / 19   ( m / s )  ,                                        B ) 15 / 8   ( m / s )  , 

C ) 25 / 9   ( m / s )  ,                                  D ) 17 / 3   ( m / s )  , 

Correct Answer : -   C ) 25 / 9   ( m / s )  ,

Solution : -

m1 = 4 kg    ,    v1 = 5 m / s  =  5 î .

m2 = 5 kg    ,    v2 = 3 m / s  =  3 ĵ .

We have formula for velocity : -

V = ( m1 v1  +  m2 v2 )  /  ( m1 + m2 )  ,

So put values in this formula : -

V = ( 4 x 5 î  +  5 x 3 ĵ )  /  ( 4 + 5 )   ,

V =  ( 20 î + 15 ĵ )  /  9  ,

V =  ( 20 î  /  9 )  +  ( 15 ĵ  /  9 ) .

So , magnitude  of  velocity  : -

| V |  =  √ ( 20 / 9 )² + ( 15 / 9 )²  ,

| V |  =  √ ( 20 )² + ( 15 )²   /   9² ,

| V |  =  25 / 9   ( m / s )  ,  Answer .

OR

 

3 ) A particle is projected from the ground with an initial speed of v at an angle of projection θ . The average velocity of particle between its time of projection and times it reaches highest point of trajectory is . . . . . . . . . . . ?

Solution : -