Analysis of Motion in 1D And 2D

Motion in One Dimension (1D)

Definition:
Motion in one dimension refers to movement along a straight path. It is the simplest form of motion, often used to analyze objects moving back and forth along the same line.

Example:
A skier slides down a 100-meter-long frictionless slope and reaches a speed of 20 m/s at the bottom. What is the angle of the slope?

Given Data:

• Slope length (dd) = 100 m

• Final velocity (vfv_f) = 20 m/s

• Initial velocity (viv_i) = 0 m/s

• Acceleration due to gravity (gg) = 9.8 m/s²

Result:
The angle of the slope is approximately 11.8°.

Key Points for 1D Motion:

• Movement occurs along a single straight line.

• Calculations involve only speed, distance, and time.

Motion in Two Dimensions (2D)

Definition:
Motion in two dimensions involves movement within a flat plane, combining horizontal and vertical components. Examples include projectile motion and objects falling while moving sideways.

Example:
A 75 kg skydiver, modeled as a rectangular box with dimensions 20 cm×40 cm×180 cm20 \, \text{cm} \times 40 \, \text{cm} \times 180 \, \text{cm}, falls feet first. What is his terminal velocity, assuming a drag coefficient (CdC_d) of 0.8 and air density (ρ\rho) of 1.2 kg/m³?

Result:
The terminal velocity of the skydiver falling feet first is approximately 138.3 m/s.

Key Points for 2D Motion:

• Involves movement along two axes (e.g., horizontal and vertical).

• Requires simultaneous consideration of motion in both directions.

• Calculations are more complex compared to 1D motion.