# Motion in 2 Dimensions

### Understanding Motion in 2 Dimensions

• Two-dimensional motion occurs when an object moves in more than one direction or along more than one axis.
• Two-dimensional motion can be analysed using vector quantities such as displacement and velocity.
• The vector quantities in two dimensions are described by their magnitude (size) and direction.
• When an object’s motion is along a curved path, it is described as projectile motion.

### Vector Quantities

• A vector is a physical quantity that has both magnitude and direction.
• Examples of vector quantities include velocity, acceleration, and displacement.
• Vectors can be represented graphically using arrows, where the length of the arrow shows the magnitude and the direction of the arrow depicts the direction of the vector.

• Vector addition is the process of combining two or more vectors.
• The resultant vector is the vector that results from vector addition, it can also be found by drawing a line from the start of the first vector to the end of the last vector.
• Vector resolution involves breaking a vector down into its component vectors along the x and y axes.

### Projectile Motion

• A projectile is an object moving under the influence of gravity while its horizontal motion remains constant.
• Horizontal and vertical motions of a projectile are independent of each other.
• The trajectory of a projectile is parabolic.
• The maximum height, range, and time of flight of a projectile can be determined using appropriate equations of motion.

### Relative Velocity

• Relative velocity refers to the velocity of one body in relation to another.
• If two objects are moving in the same direction, their relative velocity is the difference between their velocities.
• If two objects are moving in opposite directions, their relative velocity is the sum of their individual velocities.

### Newton’s Laws of Motion

• Newton’s first law (law of inertia) states that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force.
• Newton’s second law states that the rate of change of momentum of a body is directly proportional to the force applied and occurs in the direction in which the force is applied.
• Newton’s third law states that for every action, there is an equal and opposite reaction.

### Understanding Problem-Solving in Kinematics

• Questions about motion in two dimensions are typically solved by breaking the problem into horizontal and vertical components.
• Each component can be analysed separately using the principles of kinematics; thereafter, the results are combined to give the final answer.
• Use of diagrams is encouraged to help visualise and solve problems.