Question

Can you give me basic assumption about 2D
motion

Answer 1

Here are the basic assumptions and core concepts usually used when analyzing 2‑D motion (plane motion) in introductory physics:

1. Motion confined to a plane
- The object moves only in two orthogonal directions (conventionally x and y). All vectors lie in that plane.

2. Point‑particle approximation
- Treat the object as a point mass (ignore rotation and size) unless rotation matters.

3. Inertial reference frame
- Use a non‑accelerating frame so Newton’s laws apply directly.

4. Independence of orthogonal components
- Motion in x and y are treated independently (they share the same time variable). Solve kinematics separately for each component.

5. Constant (or known) acceleration components
- Often assume constant acceleration: ax and ay are known constants. Typical case: ax = 0, ay = −g (gravity).
- If acceleration varies, use vector calculus (a = dv/dt, v = dr/dt) or integrate known a(t).

6. Neglect air resistance (when simplifying)
- Many problems ignore drag so only gravity acts vertically.

Key vector and component equations (constant acceleration)
- Vector form: v = v0 + a t
- r = r0 + v0 t + (1/2) a t^2
- Component form:
- x(t) = x0 + v0x t + (1/2) ax t^2
- y(t) = y0 + v0y t + (1/2) ay t^2
- vx(t) = v0x + ax t
- vy(t) = v0y + ay t

Projectile motion (common special case: ax = 0, ay = −g)
- Initial components: v0x = v0 cosθ, v0y = v0 sinθ
- Horizontal motion: x(t) = x0 + v0 cosθ · t
- Vertical motion: y(t) = y0 + v0 sinθ · t − (1/2) g t^2
- Time of flight (launch and land at same height): T = 2 v0 sinθ / g
- Range (same launch/landing height): R = v0^2 sin(2θ) / g
- Maximum height: H = v0^2 sin^2θ / (2g)

Uniform circular motion (another 2‑D case)
- Speed may be constant, but velocity direction changes.
- Centripetal acceleration magnitude: ac = v^2 / r directed toward center.

Steps to solve typical 2‑D problems
1. Choose coordinate axes (often x horizontal, y vertical).
2. Break initial velocity into components.
3. Write component kinematic equations for x and y.
4. Use one component to find time, substitute into the other to find positions/velocities.
5. Check units and reasonableness.

Common approximations and limitations
- Point mass and no air resistance: good for basic projectile calculations but fails at high speed/long range.
- Constant g: good near Earth’s surface; not valid for large altitude changes.
- Flat Earth: ignores curvature for long distances.

If you want, I can:
- Work a specific example (e.g., projectile fired at angle θ with given speed),
- Show how to handle different launch and landing heights,
- Or include drag/variable acceleration treatments.