A $2000-\mathrm{kg}$ car moving east at $10.0 \mathrm{~m} / \mathrm{s}$ collides with a $3000-\mathrm{kg}$ car moving north. The cars stick together and move as a unit after the collision, at an angle of $40.0^{\circ}$ north of east and a speed of $5.22 \mathrm{~m} / \mathrm{s}$. Find the speed of the $3000-\mathrm{kg}$ car before the collision.