You are a traffic accident investigator. You have arrived at the scene of an accident. Two trucks of equal mass(3,000 kg each) were involved in a rear-end accident at a stop sign. here is what you know:

Truck 1 approched the intersection from the top of a 22-meter hill.
Truck 2 was on a flat stretch of road directly in front of truck 1.
At the bottom of the hill, before braking for the stop sign, Truck 1 was going 20 m/s and truck 2 was going 35 m/s.
From the skid marks on the road you can see that truck 1 applied force on its brakes for 2 seconds, 80 meters before the stop sign.
There were no skid marks left by truck 2. The collision occured at the stop sign, where truck 2 had stopped.
After the collision, both trucks were moving together in the same direction at 10 m/s, before slowly rolling to a stop.
You must now push truck 2 using 1,000 N of force, 8 meters off the side of the road so no one else gets hurt.
How much energy did Truck 1 lose in the collision?
How much energy did Truck 2 gain in the collision?

To determine the energy lost by Truck 1 and the energy gained by Truck 2 in the collision, we need to consider the principle of conservation of energy. According to this principle, the total energy before the collision should be equal to the total energy after the collision.

Let's break down the problem step by step:

1. Determine the initial kinetic energy of Truck 1 before the collision:
The initial kinetic energy of an object can be calculated using the formula:
Initial Kinetic Energy = (1/2) * mass * velocity^2

Given:
Mass of Truck 1 = 3,000 kg
Velocity of Truck 1 before braking = 20 m/s

Using the formula, we can calculate:
Initial Kinetic Energy of Truck 1 = (1/2) * 3,000 kg * (20 m/s)^2

2. Determine the initial kinetic energy of Truck 2 before the collision:
Truck 2 was already stopped, so its initial kinetic energy is zero.

Initial Kinetic Energy of Truck 2 = 0

3. Determine the final kinetic energy of both trucks after the collision:
The final kinetic energy of the trucks can be calculated using the same formula as before.

Given:
Mass of Truck 1 = 3,000 kg
Mass of Truck 2 = 3,000 kg
Velocity of both trucks after the collision = 10 m/s

Final Kinetic Energy of both trucks = (1/2) * (3,000 kg + 3,000 kg) * (10 m/s)^2

4. Calculate the energy lost by Truck 1 in the collision:
The energy lost by Truck 1 can be calculated by subtracting its final kinetic energy from its initial kinetic energy.

Energy lost by Truck 1 = Initial Kinetic Energy of Truck 1 - Final Kinetic Energy of both trucks

5. Calculate the energy gained by Truck 2 in the collision:
The energy gained by Truck 2 can be calculated by subtracting the total initial kinetic energy (including Truck 1) from the final kinetic energy of both trucks.

Energy gained by Truck 2 = Final Kinetic Energy of both trucks - (Initial Kinetic Energy of Truck 1 + Initial Kinetic Energy of Truck 2)

By following these steps and plugging in the given values, you can calculate the energy lost by Truck 1 and the energy gained by Truck 2 in the collision.

1. At the bottom of the hill, before braking for the stop sign, truck 2 was going 35 m/s. The collision occured at the stop sign, where truck 2 had stopped. >> Calculte initial momentums, and initial KEnergies.

2. After the collision, both trucks were moving together in the same direction at 10 m/s, before slowly rolling to a stop.>> Calculate the momentum of the truck combinations..
3.Now, you can determine the combined velocities, which is the same as individual velocityies. Calculate the KE of each truck after the collision.
4. calcuate the energies lost/gained during the collisions.