Question

You drive 7.50 km in a straight line in a direction 15º east of north.

Find the distances you would have to drive straight east and then straight north to arrive at the same point. (This determination is equivalent to finding the components of the displacement along the east and north directions.)


What is the component of the displacement along the east direction?
a) 7.50 {km} ⋅ cos(15^∘)
b) 7.50 {km} ⋅ sin(15^∘)
c) 7.50 {km} ⋅ tan(15^∘)
d) 7.50 {km} ⋅ cot(15^∘)

Answer 1

To find the component of displacement along the east direction, use the formula Displacement along east direction = Displacement * cos(angle). Substituting the values, we find that the answer is 7.50 km * cos(15°).

Step-by-step explanation:

To find the component of displacement along the east direction, we can use trigonometry. Let's call the north direction as the y-axis and the east direction as the x-axis. The displacement is 7.50 km, and the angle between the displacement and the north direction is 15° east of north.

The component of displacement along the east direction can be found using the formula:

Displacement along east direction = Displacement * cos(angle)

Substituting the values, we get:

Displacement along east direction = 7.50 km * cos(15°)

Simplifying this, we find that the answer is 7.50 km * cos(15°).