Trigonometry for physics (right triangles, components) Transitional Reasoning Practice

Questions

1. 1.

   During a laboratory investigation on inclined surfaces, a student sets up a straight ramp of length 2.5 m whose upper end rests at a vertical height of 1.5 m above the floor. A block weighing 20 N rests on the ramp, where the component of its weight acting parallel to the surface is given by $W_{\parallel} = W \sin\theta$, with $\theta$ representing the incline angle relative to the horizontal floor. Based on the geometric dimensions of the ramp, what is the magnitude of the parallel weight component acting on the block?

   • A) 12 N
   • B) 15 N
   • C) 16 N
   • D) 25 N
2. 2.

   A field technician anchors a portable weather station using a guy wire pulled taut with a tension of 200 N. The wire forms an angle of 30° with the vertical support pole. Using sin(30°) = 0.50 and cos(30°) = 0.87, which pair correctly gives the horizontal and vertical components of the tension force exerted on the top of the pole?

   • A) Horizontal component: 100 N; vertical component: 174 N
   • B) Horizontal component: 174 N; vertical component: 100 N
   • C) Horizontal component: 100 N; vertical component: 200 N
   • D) Horizontal component: 87 N; vertical component: 50 N

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