Math Solution of Motion in Two Dimensions

Math Solution of Motion in Two Dimensions

Galileo was the first to realize that a moving body can have several separate motions, which are independent of each other. His thinking provides a foundation for Newton’s treatment of acceleration and force.

A body moving at constant velocity can be described by a sum of velocities in two directions, typically x and y co-ordinates.

The path of a projectile may combine constant speed in the horizontal direction with acceleration due to gravity in the vertical direction. This independence of vertical and horizontal motions is counter-intuitive, and only careful teaching combined with demonstration experiments will convince students.

Math Solution of Motion in Two Dimensions

Math Solution of Motion in Two Dimensions

Math Solution of Motion in Two Dimensions

Math Solution of Motion in Two Dimensions

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Math Solution of Motion in Two Dimensions

Math Solution of Motion in Two Dimensions

Math Solution of Motion in Two Dimensions

Two dimensional motion

Galileo was the first to realize that a moving body can have several separate motions, which are independent of each other. His thinking provides a foundation for Newton’s treatment of acceleration and force.

A body moving at constant velocity can be described by a sum of velocities in two directions, typically x and y co-ordinates.

The path of a projectile may combine constant speed in the horizontal direction with acceleration due to gravity in the vertical direction. This independence of vertical and horizontal motions is counter-intuitive, and only careful teaching combined with demonstration experiments will convince students.

Accelerations have the same additive properties. They too are vectors that can be added by constructing a parallelogram. Forces too are vectors and obey the same addition rule. In other words: when several forces act on a body, each produces its own effect on motion. One force does not interfere with the motion produced by another force.

Institute of Physics

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