Final answer:
To solve two-dimensional motion problems, one must separately analyze horizontal and vertical motions, solve both using one-dimensional kinematics, and then recombine them using vector addition to find overall displacement and velocity.
Step-by-step explanation:
To solve two-dimensional motion problems, you need to analyze the motion separately in the horizontal and vertical dimensions, as each can be treated as an independent one-dimensional problem. The process involves the following steps:
- Examine the situation to determine which physical principles are involved and what is given or can be inferred from the problem (identify the knowns).
- Treat the motion as two independent one-dimensional motions: one horizontal (with no acceleration if no air resistance) and one vertical (typically with acceleration due to gravity).
- Solve for the unknowns in the two separate motions (one horizontal and one vertical), remembering that the only common variable between the motions is time t.
- Recombine the two motions to find the total displacements and velocity, using vector addition to find the magnitude and direction of the total displacement and velocity.
For the horizontal motion, velocity is a constant and the kinematic equations simplify as follows:
For the vertical motion, with gravity as the acceleration (ay = -g), the equations are more complex:
Finally, you solve for the magnitude and direction of the resultant displacement and velocity using the equations:
- S = √x² + y²
- Θ = tan⁻¹(y/x)
- v= √vx² + vy²
Keep in mind the problem-solving basics for kinematics, as you identify the physical principles involved, list knowns and unknowns, find applicable equations, solve for numerical solutions, and check if the answers are reasonable.