A roller-coaster car moves 200 ft horizontally and then...

A roller-coaster car moves $200 \mathrm{ft}$ horizontally and then rises 135 ft at an angle of $30.0^{\circ}$ above the horizontal. It next travels $135 \mathrm{ft}$ at an angle of $40.0^{\circ}$ downward. What is its displacement from its starting point? Use graphical techniques.

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Key Concepts

Displacement

Displacement is a vector quantity that represents the change in position from a starting point to an ending point. It takes into account both distance and direction, making it distinct from scalar quantities like distance traveled.

Vector Decomposition

Vector decomposition involves breaking a vector into its horizontal and vertical components using trigonometric functions such as sine and cosine. This process simplifies the analysis of vectors by allowing them to be handled component-wise.

Graphical Vector Addition

Graphical vector addition is the method of combining vectors visually by drawing them tail-to-head. This technique is especially useful to determine the overall or resultant vector, which represents the combined effect of all individual vectors.

Resultant Vector

The resultant vector is the single vector obtained by adding two or more vectors together. It encapsulates the net effect of all the individual displacements, providing both the magnitude and the direction of the overall movement.

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