Vector Operations Chapter 2.4 A

Coordinate Systems in 2 D Two methods can be used to describe motion: one axis {x-axis} two axis {x-axis; y-axis}

Coordinate Systems in 2 D 1 dimension y v = 300 m/s Northeast

Coordinate Systems in 2 D The problem with this method is that the axis must be turned again if the direction of the object changes.

Coordinate Systems in 2 D It will also become difficult to describe the direction of another object if it is not traveling exactly Northeast.

Coordinate Systems in 2 D The addition of another axis not only helps describe motion in two dimensions but also simplifies analysis of motion in one dimension.

Coordinate Systems in 2 D y x v = 300 m/s Northeast

Coordinate Systems in 2 D When analyzing motion of objects thrown into the air orienting the y-axis perpendicular to the ground and therefore parallel to the direction of the free fall acceleration simplifies things.

Coordinate Systems in 2 D There are no firm rules for applying to the coordinate system. As long as you are consistent, your final answer should be correct. This is why picking a frame of reference is extremely important.

Resultant Magnitude & Direction In order to determine the resultant magnitude and direction, we can use two different methods: 1) Pythagorean Theorem 2) Tangent Function

Resultant Magnitude & Direction The Pythagorean theorem states that for any right angle, the square of the hypotenuse (side opposite to the right angle) equals the square of the other 2 sides. c2 = a2 + b2

Resultant Magnitude & Direction Use the tangent function to find the direction of the resultant. Opposite hypotenuse adjacent tanѲ = opposite = ∆ y adjacent ∆ x