132k views
1 vote
2.2 VECTORS IN TWO 120 N bearing 70° and 160 N bearing 40°


1 Answer

4 votes

Answer:

Step-by-step explanation:

Assuming you want to find the resultant vector of the two given vectors:

We can use the graphical method or the component method to find the resultant vector. Here, I will demonstrate the component method:

Step 1: Convert the given vectors into their component form (i.e., horizontal and vertical components).

Vector 1: 120 N bearing 70°

Horizontal component = 120 cos(70°) ≈ 38.23 N

Vertical component = 120 sin(70°) ≈ 113.41 N

Vector 2: 160 N bearing 40°

Horizontal component = 160 cos(40°) ≈ 122.15 N

Vertical component = 160 sin(40°) ≈ 103.08 N

Step 2: Add the horizontal components and vertical components separately to get the components of the resultant vector.

Horizontal component of resultant vector = 38.23 N + 122.15 N ≈ 160.38 N

Vertical component of resultant vector = 113.41 N + 103.08 N ≈ 216.49 N

Step 3: Use the Pythagorean theorem to find the magnitude of the resultant vector.

Magnitude of resultant vector = √(160.38 N)^2 + (216.49 N)^2 ≈ 268.15 N

Step 4: Find the direction of the resultant vector.

Direction of resultant vector = tan^-1(216.49 N / 160.38 N) ≈ 53.12°

Therefore, the resultant vector of the two given vectors is approximately 268.15 N at a bearing of 53.12°.

User Alex Humphrey
by
8.5k points