3.1 Kinematics in Two Dimensions: An Introduction

3.1 Kinematics in Two Dimensions: An Introduction

  • Explain the properties of a projectile, such as gravity, range, maximum height, and trajectory.
  • The principle of independence of motion can be applied to solve projectile motion problems.
  • Relative velocity is determined by the principles of vector addition.
  • The arcs of a basketball, a satellite, a bicycle, a swimmer, and a puppy are a few examples of motions along curved paths.
    • Most motions in nature follow curved paths.
    • The motion of a ball on a pool table or a skater on an ice rink is described by two-dimensional kinematics.
    • A car following a winding mountain road is described by three-dimensional kinematics.
    • The two- and three-dimensional kinematics are extensions of the one-dimensional kinematics that were developed for straight-line motion.
    • This simple extension will allow us to apply physics to many more situations, and it will also give us unexpected insights about nature.
  • In a city like New York, it's rare for walkers and drivers to travel in straight lines.
    • They must follow the roads and sidewalks.
  • The blocks are the same size in this scene.
  • You are forced to take a two-dimensional path because the straight-line path that a helicopter might fly is blocked to you as a pedestrian.
    • You walk 14 blocks, 9 east and 5 north.
  • The shortest distance between two points is a straight line, according to an old adage.
    • The Pythagorean theorem can be used to find the straight-line distance because the two legs of the trip form a right triangle.
  • The hypotenuse is related to the length of the legs of a right triangle.
    • The relationship is given by something.
  • The length of the triangle in units of city blocks is considerably shorter than the 14 blocks you walked.
    • It appears that "9" and "5" have only one digit.
  • The 14 blocks walked by the pedestrian are larger than the straight-line path followed by a helicopter.
  • The blocks are the same size.
  • We use arrows to represent the one-dimensional kinematics.
    • The length of the arrow is related to the magnitude of the object.
  • The straight-line path is given by the horizontal and vertical components of the motion.
    • The first shows a displacement east.
    • The second is a displacement north.
    • The third vector has a total displacement of more than 10 blocks.
    • There is a straight-line path between the two points.
    • The right triangle is formed by the vectors that are perpendicular to each other.
    • The magnitude of the total displacement can be calculated using the Pythagorean theorem.
    • His or her motion eastward affects how far he or she walks.
    • How far he or she walks north is dependent on his or her motion northward.
  • The horizontal and vertical parts of motion are not related.
    • Motion in the horizontal direction does not affect motion in the vertical direction.
  • This is true if you walk in one direction first, followed by another.
    • It's true of more complicated motion that involves movement in two directions at the same time.
    • Let's compare the motions of two baseballs.
    • A baseball is dropped.
    • One is thrown from the same height and the other follows a curved path.
    • The balls are captured by a stroboscope as they fall.
  • The motions of two identical balls are shown in this picture.
    • Each position has an equal time interval.
    • The horizontal and vertical velocities are represented by the arrows.
    • The ball on the right has a higher initial horizontal velocity than the ball on the left.
    • The vertical velocities and positions are the same for both balls.
    • The motions of the vertical and horizontal are independent.
  • The vertical positions of the two balls are the same for each flash of the strobe.
    • The similarity shows that the vertical motion is not dependent on whether the ball is moving horizontally or not.
    • Careful examination of the ball shows that it travels the same distance between flashes.
    • There are no additional forces on the ball in the horizontal direction after it is thrown.
    • The result means that the horizontal velocity is unaffected by either vertical motion or gravity.
    • The case is only true for ideal conditions.
    • Air resistance will affect the speed of the balls.
  • There are two independent one-dimensional motions in the path of the ball.
    • The key to analyzing projectile motion is to break it into motions.