Approximate the horizontal and vertical components of the vector that is described. (Round your answers to two decimal places.)

Question

Approximate the horizontal and vertical components of the vector that is described. (Round your answers to two decimal places.)

A child pulls a sled through the snow by exerting a force of 30 pounds at an angle of 50° with the horizontal.

horizontal=     lb 

vertical =.  lb 

Answer 1

In the triangle, we can use trig ratios to solve for the force component in the x-direction (F_x) and the force component in the y-direction (F_y)

cos(θ) = adjacent/hypotenuse so cos(θ) = F_x/F meaning that F_x = Fcos(θ) or in this case:

F_x = 30cos(50°) = 19.28 pounds

sin(θ) = opposite/hypotenuse so sin(θ) = F_y/F meaning that F_y = Fsin(θ) or in this case:

F_y = 30sin(50°) = 22.98 pounds

Answer 2

Draw the vector in the first quadrant with magnitude 30 pounds, initial point (0,0), and so that the angle formed by the positive x-axis and the vector is 50°. The vector is the hypotenuse of a right triangle with horizontal leg (horizontal component) 30cos50° and vertical leg (vertical component) 30sin50°.

Answer 3

Approximate the horizontal and vertical components of the vector that is described. (Round your answers to two decimal places.)

A child pulls a sled through the snow by exerting a force of 30 pounds at an angle of 50° with the horizontal.

horizontal=30 Cos 50     lb 

vertical =.30 Sin 50 lb 

Plug in Cos 50 =0.642= 0.64

Sin 50=0.766= 0.77