Question

Carolina rides her sled down a 28 meter hill which has a 75 degree decline from the horizontal. Express her horizontal and vertical displacement as a linear combination of vectors in (ai + bj) form.

A) 28 cos75 m ⋅ i + 28 sin75 m ⋅ j
B) 28 sin75 m ⋅ i + 28 cos75 m ⋅ j
C) 28 cos15 m ⋅ i + 28 sin15 m ⋅ j
D) 28 sin15 m ⋅ i + 28 cos15 m ⋅ j
E) 28 cos75 m ⋅ i + 28 cos15 m ⋅ j

Answer 1

Carolina's displacement given a 75-degree hill decline is best represented as a linear combination of vectors in the form (28 sin75 m · i + 28 cos75 m · j).

Step-by-step explanation:

The task is to express Carolina's horizontal and vertical displacement as a linear combination of vectors in (ai + bj) form, where Carolina rides her sled down a hill with a 75-degree decline from the horizontal. The correct expression for her displacement in vector form is Option B: 28 sin75 m · i + 28 cos75 m · j, where i represents the horizontal component, and j represents the vertical component. The sine function is used for the horizontal component because the decline is from the horizontal, and the cosine function is used for the vertical component.