Final answer:
To estimate Car 2's speed before the collision, the work done by the stopping force that is 0.7 times the combined weight of the cars over a 6-meter distance can be set equal to the initial kinetic energy of Car 2. Solving the resulting equation will give the speed of Car 2 at impact.
Step-by-step explanation:
Calculating the Speed of Car 2 Before Collision
To determine the estimated speed of Car 2 just before the collision, we can use the work-energy principle. Since both cars have identical mass and after the collision, they move together, we know that the momentum is transferred from Car 2 to Car 1. The frictional force, which is 0.7 times the combined weight of the cars, works to stop the cars over a distance of 6 meters. This force does negative work, reducing their kinetic energy to zero.
The force of friction can be calculated using the equation: F = μ × w, where μ is the coefficient of friction and w is the weight of the cars. The work done by friction is then W = F × d, where d is the distance over which the force is applied.
The initial kinetic energy of the system, which is all due to Car 2 since Car 1 is at rest, must equal the work done by the force of friction. So, ½ mv² = Fd. Solving for v, the initial velocity of Car 2, gives us the speed just before impact. We can solve this equation for v since μ, d, and the mass of the cars (via their combined weight) are known.
In conclusion, by knowing the stopping force as a function of weight and the distance over which the cars skidded, we can calculate the initial speed of Car 2 using the principles of conservation of energy and the work-energy theorem.