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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.

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