A particle moves in the x y -plane under the action of a force F such that the components of its linear momentum p at any time t are p_x=2 t, p_y= t . The angle between F and p at time t is

Step-by-step solution

aligned & p_x=2 t, p_y=2 t & aligned & p =p_x i +p_y j &=2 t i +2 t j aligned & Force = rate of change of momentum & = d p d t aligned aligned & F =-2 t i +2 t j & = F p | F | | p | & = (-2 t i +2 t j )(2 t i +2 t j ) 4 ^2 t+4 ^2 t 4 ^2 t+4 ^2 t & =0 & =90^ aligned