To find the initial speed of the van in a collision with a compact car, the conservation of momentum principle is applied. The total momentum before the collision equals the total momentum after the collision, which is expressed in the equation: (mass of van * initial speed of van) + (mass of car * initial speed of car) = (total mass after collision * final speed). Given the masses and the final speed of 8.5 m/s, the initial speed of the van can be calculated as 11.2 m/s. This approach effectively uses the momentum conservation equation to solve for the unknown initial speed.
