Two-dimensional Kinematics

Explanation
Displacement refers to the change in position of an object, specifically the distance and direction from the initial position to the final position. It is a vector quantity that takes into account both magnitude and direction. Velocity, on the other hand, refers to the rate at which an object changes its position, taking into account both speed and direction. Rate is a general term that can refer to various types of measurements or changes. Therefore, the correct answer for the given question is displacement.

Explanation
Acceleration is the correct answer because it refers to the change in velocity over time. It measures how quickly an object's velocity is changing, either by speeding up, slowing down, or changing direction. Speed refers to the rate at which an object moves, while distance is the total length traveled. Therefore, acceleration is the most appropriate term to describe the change of velocity over time.

Explanation
An object in free-fall is undergoing constant acceleration because the acceleration due to gravity remains constant throughout the motion. This means that the object's velocity increases by the same amount every second.

Explanation
The acceleration due to gravity at or near the earth's surface is 9.8 m/s2. This value is commonly referred to as "g" and represents the rate at which an object falls towards the earth. It is a constant value that is used in many physics calculations and is an important factor in understanding the motion of objects in free fall.

Explanation
Displacement in 2-dimensions is a vector because it requires both magnitude (the length or size of the displacement) and direction (the angle or orientation of the displacement). Scalars, on the other hand, only have magnitude and do not have direction. Therefore, displacement in 2-dimensions cannot be a scalar or any of the other options given.

Explanation
A vector in 2-dimensions can be broken down into horizontal and vertical component vectors. This means that the vector can be represented as the sum of two vectors, one pointing in the horizontal direction and the other pointing in the vertical direction. The components represent the magnitude and direction of the vector in each respective direction.

Explanation
The vertical component of velocity can be found using the formula v * sin(theta), where v is the magnitude of the velocity and theta is the angle. In this case, the magnitude of the velocity is 5 m/s and the angle is 30 degrees. Therefore, the vertical component of velocity is 5 * sin(30) m/s.

Explanation
If we ignore air resistance, the only force acting on a projectile in the horizontal direction is its initial velocity. Since there are no other forces causing acceleration in the horizontal direction, the horizontal component of acceleration is considered to be zero.

Explanation
The vertical component of acceleration of a projectile is -9.8 m/s^2. This is because the force of gravity acts in the downward direction and causes the projectile to accelerate downwards at a constant rate of 9.8 m/s^2.

Explanation
The launch angle of 45 degrees will result in the greatest horizontal displacement of a projectile when the initial velocity does not change. This is because at this angle, the vertical and horizontal components of the initial velocity are equal. As a result, the projectile will spend an equal amount of time in the air and cover the same horizontal distance for each second of flight. Therefore, the projectile will travel the farthest horizontally at this launch angle compared to the other angles given.