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The question describes two objects being dropped and thrown from the same point above the ground. A 1-kilogram object is thrown horizontally, while a 2-kilogram object is dropped vertically. We are asked to determine which quantity will be the same for both objects at any given instant.

**Key point**: Both objects experience free fall under the influence of gravity.

### Analysis:
1. **Momentum**: Momentum is given by \( p = mv \), where \( m \) is mass and \( v \) is velocity. Since the masses and velocities of the two objects differ, their momenta will also differ.

2. **Kinetic Energy**: Kinetic energy is given by \( KE = \frac{1}{2}mv^2 \). Since the objects have different masses and velocities, their kinetic energies will be different at any given instant.

3. **Height**: Both objects are released from the same height above the ground. At any given instant, they will be at the same height because both experience the same vertical acceleration due to gravity (ignoring air resistance).

4. **Total Velocity**: The velocity of each object is a combination of horizontal and vertical components. The horizontally thrown object has a horizontal velocity component that the vertically dropped object lacks. Therefore, the total velocities will be different.

### Correct Answer: 
**C. Height**

Both objects will be at the same height at any given instant.

Would you like further details or have any questions?

Here are 5 related questions:
1. How does gravity affect the motion of two objects with different masses?
2. What role does horizontal velocity play in projectile motion?
3. How do we calculate the total velocity of an object in two-dimensional motion?
4. What factors influence the momentum of an object in motion?
5. How can we determine the time it takes for an object to reach the ground from a specific height?

**Tip**: In free-fall problems, objects dropped from the same height experience the same gravitational acceleration, regardless of their mass.

A 1-kilogram object is thrown horizontally and a 2-kilogram object is dropped vertically at the same instant and from the same point above the ground. Which of the following will be the same for both objects at any given instant? 
A. Momentum 
B. Kinetic energy 
C. Height 
D. Total velocity

Understand how two objects—one thrown horizontally and one dropped vertically—experience free fall. This problem explores key physics concepts like momentum, kinetic energy, and gravitational acceleration. Suitable for Grades 9-12.

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