Roller coaster problem. Vectors.

[mrrocketknigh]

Homework Statement

A roller coaster moves 200 ft horizontally and then rises 135 ft at an angle of 30(degrees) above the horizontal. Next, it travels 135 ft at an angle of 40(degrees) below the horizontal. Use graphical techniques to find the roller coaster's displacement from its starting point to the end of this movement.

Homework Equations

Knowing the properties of vectors. The ANSWER SHOULD BE 421 ft at 3(degrees) below the horizontal.

The Attempt at a Solution

I don't know what to do... Please help.

 

[AvroArrow]

There are several ways to solve this problem. One way is to use the graphical technique of vector addition. Draw a diagram of the situation, with the starting point at the origin. Then draw the two vectors representing the movements of the roller coaster, with arrows pointing in the direction of movement and labels indicating the magnitude and direction of each vector. The first vector will have a magnitude of 200 ft and an angle of 30 degrees above the horizontal. The second vector will have a magnitude of 135 ft and an angle of 40 degrees below the horizontal. Next, add the two vectors together. This will give you the magnitude and direction of the overall displacement. The result should be a vector with a magnitude of 421 ft and an angle of 3 degrees below the horizontal.