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

Questions

1. 1.

   A force vector has a magnitude of 60 N and is directed at an angle of $30^\circ$ above the horizontal. What is the magnitude of its vertical component?

   • A) 52 N
   • B) 60 N
   • C) 120 N
   • D) 30 N
2. 2.

   A hiker walks such that her net displacement has an eastward component of 5.0 km and a northward component of 12.0 km. What is the magnitude of her resultant displacement?

   • A) 7.0 km
   • B) 11.0 km
   • C) 13.0 km
   • D) 17.0 km
3. 3.

   A displacement vector has a magnitude of 12 m and points at an angle $\theta$ above the positive $x$-axis. If the $x$-component of the displacement is 6.0 m, what is the angle $\theta$?

   • A) $30^\circ$
   • B) $60^\circ$
   • C) $45^\circ$
   • D) $75^\circ$
4. 4.

   A ball is launched with an initial velocity at an angle of $60^\circ$ above the horizontal. If the horizontal component of the velocity is 15 m/s, what is the magnitude of the ball's initial velocity?

   • A) 30 m/s
   • B) 7.5 m/s
   • C) 15 m/s
   • D) 60 m/s
5. 5.

   A displacement vector has a horizontal component of 7.0 m and a vertical component of 7.0 m. What angle does this vector form with the positive horizontal axis?

   • A) 30°
   • B) 45°
   • C) 60°
   • D) 90°
6. 6.

   A crate is pulled across a flat floor by a rope exerting a force of 100 N at an angle above the horizontal. If the horizontal component of this force is 80 N, what is the magnitude of its vertical component?

   • A) 60 N
   • B) 20 N
   • C) 128 N
   • D) 75 N
7. 7.

   A ramp has a horizontal run of 4.0 m and rises to a vertical height of 3.0 m. What is the value of $\sin\theta$, where $\theta$ is the angle of inclination of the ramp relative to the horizontal?

   • A) 0.75
   • B) 0.80
   • C) 0.60
   • D) 1.33
8. 8.

   A force vector of magnitude 50 N makes an angle of $30^\circ$ with the positive $y$-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