The law of conservation of matter states that matter cannot be created or destroyed in a chemical reaction. This implies that the total mass of reactants before the reaction must be equal to the total mass of products after the reaction. When gasoline burns, it reacts with oxygen to produce water vapor and carbon dioxide. Therefore, for the law of conservation of matter to hold true, the combined mass of the gasoline and oxygen (the reactants) must be equal to the combined mass of the water vapor and carbon dioxide (the products).
References:
* Integrated Physical Sciences textbooks and resources on chemical reactions and the law of conservation of matter.
* Standard chemistry principles regarding mass conservation in reactions.

As comets approach the Sun, the increased solar radiation causes the ice within the comet to evaporate (a process called sublimation), releasing gas and dust particles. This creates a visible atmosphere called a coma, and the solar wind then blows this material away from the comet, forming a tail. The tail always points away from the Sun due to the force of the solar wind. References:
* NASA's Comet Exploration Missions
* "Cometary Physics" - European Space Agency Publications

*Gravitational force comparison:** Planet X has less gravity than Planet Y. - **Acceleration due to force:** The acceleration of an object is given by \( a = \frac{F}{m} \). With the same force applied, the acceleration will be higher where the gravitational pull is weaker. - **Initial acceleration:** Since Planet X has less gravity, the same force will cause the ball to accelerate more on Planet X than on Planet Y. - **Conclusion:** The ball will initially accelerate more on Planet X. **References:** Physics textbooks on Newton's laws of motion, principles of gravitation, and kinematics.

When a man hits a ball directly upward with a stick, the kinetic energy imparted to the ball is converted into gravitational potential energy as the ball rises. As the ball reaches its highest point, its kinetic energy decreases to zero, and all of its energy is stored as gravitational potential energy. References:
* Integrated Physical Sciences, Chapter 5: Energy Transformations

**Assumption:** The collision is completely elastic, meaning no kinetic energy is lost. - **Principles of elastic collisions:** In an elastic collision, both momentum and kinetic energy are conserved. - **Velocity changes:** When two identical cars collide elastically, the car that was moving faster (rear car) will transfer some of its kinetic energy to the slower-moving car (front car). As a result, the rear car slows down, and the front car speeds up. - **Conclusion:** The velocities of the two cars will change such that the front car speeds up and the rear car slows down after the collision. **References:** Textbooks on classical mechanics, principles of conservation of momentum and energy, and problem-solving resources on elastic collisions.