Question

Draw each of the following vectors, then find its x - and y-components. a. d=(100 m,45∘ below +x-axis )

b. v=(300 m/s,20∘ above +x-axis )
c. a=(5.0 m/s²,−y-direction )

Answer 1

To draw each vector and find its x- and y-components, we can use the given magnitudes and angles. Vector d has a magnitude of 100 m and is at an angle of 45 degrees below the +x-axis. Vector v has a magnitude of 300 m/s and is at an angle of 20 degrees above the +x-axis. Vector a has a magnitude of 5.0 m/s² and is in the -y-direction.

Step-by-step explanation:

To draw each vector and find its x- and y-components, we can use the given magnitudes and angles. Let's go through each vector.

a. Vector d has a magnitude of 100 m and is at an angle of 45 degrees below the +x-axis. To draw it, start from the origin (0,0) and go 100 units in length at an angle of 45 degrees below the x-axis. The x-component can be found using Ax = Acosθ, which gives Ax = 100 cos(45°) = 70.71 m. The y-component can be found using Ay = Asinθ, which gives Ay = 100 sin(45°) = -70.71 m.

b. Vector v has a magnitude of 300 m/s and is at an angle of 20 degrees above the +x-axis. To draw it, start from the origin (0,0) and go 300 units in length at an angle of 20 degrees above the x-axis. The x-component can be found using Ax = Acosθ, which gives Ax = 300 cos(20°) = 283.46 m/s. The y-component can be found using Ay = Asinθ, which gives Ay = 300 sin(20°) = 102.54 m/s.

c. Vector a has a magnitude of 5.0 m/s² and is in the -y-direction. To draw it, start from the origin (0,0) and go -5.0 units in the y-direction. The x-component of vector a is 0 m/s² because it does not have any horizontal component.