Trigonometry for physics (right triangles, components) Knowledge-Based Practice

Questions

1. 1.

   The horizontal component of a velocity vector is $\sqrt{3}$ times as large as its vertical component. If the vector lies in the first quadrant, what angle does it make with the horizontal axis?

   • A) $60^\circ$
   • B) $45^\circ$
   • C) $15^\circ$
   • D) $30^\circ$
2. 2.

   A force vector has a magnitude of $25\text{ N}$ and a vertical component of $15\text{ N}$. What is the magnitude of its horizontal component?

   • A) $10\text{ N}$
   • B) $20\text{ N}$
   • C) $5\sqrt{34}\text{ N}$
   • D) $40\text{ N}$
3. 3.

   A force vector has a magnitude of $20\text{ N}$ and a vertical component of $10\sqrt{3}\text{ N}$. If the vector lies in the first quadrant, what angle does it make with the horizontal axis?

   • A) $30^\circ$
   • B) $60^\circ$
   • C) $45^\circ$
   • D) $90^\circ$
4. 4.

   A displacement vector has a magnitude of 60 m and is directed at an angle of $120^\circ$ measured counterclockwise from the positive x-axis. What is the horizontal component of this displacement vector?

   • A) $-30\text{ m}$
   • B) $+30\text{ m}$
   • C) $-30\sqrt{3}\text{ m}$
   • D) $+30\sqrt{3}\text{ m}$
5. 5.

   A force vector has perpendicular components of 5 N along the horizontal axis and 12 N along the vertical axis. What is the magnitude of the total force vector?

   • A) 7 N
   • B) 17 N
   • C) 169 N
   • D) 13 N
6. 6.

   A displacement vector is directed at an angle of 60° above the horizontal. If its horizontal component has a magnitude of 12 m, what is the magnitude of its vertical component?

   • A) $4\sqrt{3}$ m
   • B) 12 m
   • C) 24 m
   • D) $12\sqrt{3}$ m
7. 7.

   An airplane climbs at a constant angle of $30^\circ$ above the horizontal. If the airplane gains an altitude of $1500\text{ m}$, what is the total distance it has traveled along its flight path?

   • A) $750\text{ m}$
   • B) $1732\text{ m}$
   • C) $2598\text{ m}$
   • D) $3000\text{ m}$
8. 8.

   A velocity vector has a horizontal component of $10\text{ m/s}$ and a vertical component of $10\sqrt{3}\text{ m/s}$. What is the angle of this vector with respect to the horizontal?

   • A) $60^\circ$
   • B) $30^\circ$
   • C) $45^\circ$
   • D) $75^\circ$
9. 9.

   A force vector with a magnitude of 50 N acts at an angle of $30^\circ$ with respect to the vertical axis. What is the magnitude of the horizontal component of this force?

   • A) 25 N
   • B) 43.3 N
   • C) 28.9 N
   • D) 50 N

Answers and step-by-step solutions appear after you finish the test.