1. 2-D M OTION Physics 111

2. Y OU ARE ADDING VECTORS OF LENGTH OF 20 AND 40 UNITS. W HAT IS THE ONLY POSSIBLE RESULTANT MAGNITUDE ? A)18 B) 37 C) 64 D) 100

3. A NSWER : 37 If scalar, Max value is 60 units If scalar, min value is 20 Says the value is a Vector, so have different directions Has to be between 60 and 30 37 Is the only option that works

4. A DDING V ECTORS Add the following vectors and determine the resultant. 5.0 m/s, 45 deg and 2.0 m/s, 180 deg

5. M AG : 3.85 A T 66.5 DEGREES FROM – X AXIS

6. A DD THE FOLLOWING VECTORS AND DETERMINE THE RESULTANT. 3.0 m/s, 45 deg and 5.0 m/s, 135 deg and 2.0 m/s, 60 deg

7. A NSWER : 7.40 M / S @ 93.2 DEGREES

8. P ROBLEM : During the Vector Addition lab, Mac and Tosh start at the classroom door and walk 40.0 m, north, 32.5 m east, 15.5 m south, 68.5 m west, and 2.5 m, north. Determine the magnitude and direction of the resultant displacement of Mac and Tosh.

9. A NSWER : 45.0 m, 36.9° N

10. G IVEN THAT A + B = C, AND THAT L A L 2 + L B L 2 = L C L 2, HOW ARE VECTORS A AND B ORIENTED WITH RESPECT TO EACH OTHER ? 1 ) they are perpendicular to each other 2) they are parallel and in the same direction 3) they are parallel but in the opposite direction 4) they are at 45° to each other 5) they can be at any angle to each other

11. A NSWER : T HE ARE PERPENDICULAR Vectors satisfy the Pythagorean Theorem, with suggest they are a right triangle, where a and b would be perpendicular at a 90 degree angle

12. G IVEN THAT A + B = C, AND THAT L A L + L B L = L C L, HOW ARE VECTORS A AND B ORIENTED WITH RESPECT TO EACH OTHER ? 1) they are perpendicular to each other 2) they are parallel and in the same direction 3) they are parallel but in the opposite direction 4) they are at 45° to each other 5) they can be at any angle to each other

13. A NSWER : P ARALLEL BUT IN SAME DIRECTION The only time vector magnitudes will simply add together is when the direction does not have to be taken into account

14. A CERTAIN VECTOR HAS X AND Y COMPONENTS THAT ARE EQUAL IN MAGNITUDE. W HICH OF THE FOLLOWING IS A POSSIBLE ANGLE FOR THIS VECTOR, IN A STANDARD X - Y COORDINATE SYSTEM ? 1) 30° 2) 180° 3) 90° 4) 60° 5) 45°

15. ANSWER : 45 The angle of the vector is given by tan  = y/x. Thus, tan  = 1 in this case if x and y are equal, which means that the angle must be 45°.