Practice Exercises - Vectors - AP Physics 1 Premium
Multiple-Choice
1. A vector is given by its components, Ax = 2.5 and Ay = 7.5. What angle does vector 
make with the positive x-axis?
(A) 72°
(B) 18°
(C) 25°
(D) 50°
2. Which pair of vectors could produce a resultant of 35?
(A) 15 and 15
(B) 20 and 20
(C) 30 and 70
(D) 20 and 60
3. A vector has a magnitude of 17 units and makes an angle of 20° with the positive x-axis. The magnitude of the horizontal component of this vector is
(A) 16 units
(B) 4.1 units
(C) 5.8 units
(D) 50 units
4. As the angle between a given vector and the horizontal axis increases from 0° to 90°, the magnitude of the vertical component of this vector
(A) decreases
(B) increases and then decreases
(C) decreases and then increases
(D) increases
5. Vector .png)
has a magnitude of 10 units and makes an angle of 30° with the horizontal x-axis. Vector 
has a magnitude of 25 units and makes an angle of 50° with the negative x-axis. What is the magnitude of the resultant of these two vectors?
(A) 20
(B) 35
(C) 15
(D) 25
6. Two concurrent vectors have magnitudes of 3 units and 8 units. The difference between these vectors is 8 units. The angle between these two vectors is
(A) 34°
(B) 56°
(C) 79°
(D) 113°
7. Which of the following sets of displacements have equal resultants when performed in the order given?
I. 6 m east, 9 m north, 12 m west
II. 6 m north, 9 m west, 12 m east
III. 6 m east, 12 m west, 9 m north
IV. 9 m north, 6 m east, 12 m west
(A) I and IV
(B) I and II
(C) I, III, and IV
(D) I, II, and IV
8. Which vector represents the direction of the two concurrent vectors shown below?
9. Three forces act concurrently on a point P as shown below. Which vector represents the direction of the resultant force on point P?
10. On a baseball field, first base is about 30 m away from home plate. A batter gets a hit and runs toward first base. She runs 3 m past the base and then runs back to stand on it. The magnitude of her final displacement from home plate is
(A) 27 m
(B) 30 m
(C) 33 m
(D) 36 m
Free-Response
1. Find the magnitude and direction of the two concurrent forces shown below using the algebraic method of components.
Note: Figure is not drawn to scale.
2. Two vectors, .png)
and .png)
, are concurrent and attached at the tails with an angle θ between them. Given that each vector has components Ax, Ay and Bx, By, respectively, use the law of cosines to show that
3. Give a geometric explanation for the following statement: “Three vectors that add up to zero must be coplanar (that is, they must all lie in the same plane).”
4. (a) Is it necessary to specify a coordinate system when adding two vectors?
(b) Is it necessary to specify a coordinate system when forming the components of a vector?
5. Can a vector have zero magnitude if one of its components is nonzero?
