Physics Section 3.2 Resolve vectors into their components When a person walks up the side of a pyramid, the motion is in both the horizontal and vertical directions. A right triangle is formed by the motion of the person.

Formulas for right triangles

examples A tourist walks up a pyramid. The pyramid is 60.0 m high and 80.0 m wide. Find the displacement of the tourist.

Student problem: While following the directions on a treasure map, a pirate walks 45.0 m north and then walks 7.50 m east. What single straight line displacement could the pirate have taken?

Components of a vector are two vectors (usually perpendicular) that have the same total effect as the original vector. Breaking a vector into its components is called resolving the vector. Find the vertical and the horizontal components of a missile traveling with a velocity of 120 m/s at an angle of 30 degrees above the horizontal.

How fast must a truck travel to stay beneath an airplane that is moving 105 km/h at an angle of 25 degrees to the ground? Student problems page 92, #3,#4

It is not possible to use the Pythagorean Theorem to find the resultant of two vectors that do not act at right angles to each other. Instead to add the vectors, we must find their components. Find the resultant of forces of 25 N at 40 degrees N of E and 15 N at 35 degrees S of E.

Steps to add two or more vectors using components 1.Determine the angle θ(measured from the positive x axis counterclockwise) and the magnitude(length of vector) of each vector. 2.Calculate the x and y components of each vector. x = r cos θ y = r sin θ 3.Add the corresponding components of the vectors. (find x T and y T ) 4.Find the magnitude of the resultant using: 5. Find the angle using tan θ = y/x

Example Find the resultant of 20.0 m/s at 28 degrees west of north and 30.0 m/s at 45 degrees south of west. Student practice worksheet

Assignment Page 94 Problems 2,3,4