Two bodies of mass 1 kg and 3 kg have position vectors $$\widehat i + 2\widehat j + \widehat k$$ and $$ - 3\widehat i - 2\widehat j + \widehat k$$, respectively. The center of mass of this system has a position vector :

A particle of mass m is projected with velocity v making an angle of 45^o with the horizontal. When the particle lands on the level ground the magnitude of the change in its momentum will be :

A shell of mass 200 gm is ejected from a gun of mass 4 kg by an explosion that generates 1.05 kJ of energy. The initial velocity of the shell is :

A 0.5 kg ball moving with a speed of 12 m/s strikes a hand wall at an angle of 30^o with the wall. It is reflected with the same speed at the same angle. If the ball is in contact with the wall for 0.25 seconds, the average force acting on the wall is :