Physics

• Two-dimensional motion

  Motion in a plane where the object moves in both the x and y direction simultaneously
• Describing two-dimensional motion


  1. Use vector concept

  2. Object moves along a curved path between points P and Q

  3. Displacement vector from P to Q is AF

  4. Perpendicular components of AF are Ax and Ay
• Magnitude of displacement vector AF

  √(Ax)²+(Ay)²
• Direction of displacement vector AF

  tan⁻¹(Ay/Ax)
• An object moving with constant speed along a curved path is accelerating as the direction of the velocity is changing
• The direction of the velocity of the object is tangential to its path
• The object is accelerated whenever the velocity changes in magnitude, direction, or both
• Projectile


  Any object that is thrown, shot, or launched through the air and follows a curved path under the influence of gravity
• Projectile motion


  1. Curved path

  2. Displacement

  3. Tangential velocity

  4. Acceleration
• Projectile


  Any object thrown into space upon which the only acting force is the gravity
• Trajectory


  The path followed by a projectile
• Projectile motion


  The motion of an object moving in both horizontal x direction and vertical y direction simultaneously
• Projectile motion (when air resistance is neglected)

  • Object moves along the horizontal x direction with a constant velocity
  • Object moves in the vertical y direction with constant downward acceleration
  • Only gravitational force is acting on it
  • Downward acceleration is the acceleration due to gravity g which is a constant over the range of motion
  • Vertical motion is a free fall motion
• Initial velocity (v₀)


  If the initial velocity makes an angle θ with the horizontal, the x and y components of the initial velocity are v₀x=v₀cos θ and v₀y=v₀sin θ
• Time of flight


  Twice the time to reach the maximum height
• Projectile motion of an object thrown horizontally

  No vertical component to its initial velocity (v₀y=0, v₀x=v₀)<|>Velocity in the y direction is v₀y=-gt (downward)<|>Vertical displacement in time t is y=-1/2gt²
• When two forces act on an object simultaneously, they produce a resultant force that has both magnitude and direction.
• Work done on an object increases its kinetic energy, while work done against friction decreases it.