The figure is below.
a) The difference of the two vectors,
`Delta(P) = P_f -P_i`
is found by drawing the two vectors (initial and final momentum) from the same point. The above difference is the vector drawn from the origin the second vector of the difference (`P_i` ) to the tip of the first vector (`P_f` ).
Initial momentum components are
`P_(ix) =P_i*cos(alpha) =m*v_i*cos(45) =2*0.707*cos(45) = 1 kg*m/s`
`P_(iy) =P_i*sin(alpha) =m*v_i*sin(45) =2*0.707*sin(45) = 1kg*m/s`
Thus as a vector `P_i =1*hatx+1*haty` `kg*m/s`
Final momentum components are
`P_(fx) =0 kg*m/s`
`P_(fy) =1 kg*m/s`
Thus as a vector `P_f = 0*hatx +1*haty` `kg*m/s`
The difference between final and initial impulse is
`Delta(P) =P_f-P_i = (0*hatx +1*haty)-(1*hatx+1*haty) =-1*hatx [kg*m/s]` ` `
c) As the momentum theorem says the external applied force is equal to the variation of the momentum over the time.
`F = (Delta(P))/(Delta(t)) =-(1*hatx)/(Delta(t))`
The direction of the blow was horizontal from right to left.