Answer
a) The final velocity of the car is $-0.43m/s$
b) The final velocity of the van is $+1.81m/s$
Work Step by Step
The van, whose mass $M=1055kg$ and initial velocity $V_0=0$, is hit by the car, whose mass $m=715kg$ and initial velocity $v_0=+2.25m/s$
1) The collision is elastic, so the total kinetic energy is conserved: $$\frac{1}{2}(MV_0^2+mv_0^2)=\frac{1}{2}(MV_f^2+mv_f^2)$$ $$1055V_f^2+715v_f^2=0+(715\times2.25^2)=3619.69\ (1)$$
2) The total momentum is conserved, too: $$MV_0+mv_0=MV_f+mv_f$$ $$1055V_f+715v_f=0+(715\times2.25)=1608.75\ (2)$$
Solving (1) and (2), we have $V_f=+1.81m/s$ and $v_f=-0.43m/s$, which are the final velocities of the van and the car, respectively.
