Question

A sled is being pulled across a floor by two ropes such that the angle between them is 40°. If the forces on the ropes are 100 pounds and 150 pounds, what is the resultant of the forces?
98 lb
192 lb
228 lb
236 lb

Answer 1

Answer:

option 4 ⇒ 236 lb.

Step-by-step explanation:

Best explanation of the question is as shown in the attached figure.

we will use the parallelogram method to calculate resultant force.

to get the length of the resultant force ⇒ use the cosines law

The cosine law is a² = b² + c² - 2 * b * c * cos (∠A)

Applying at the question where b = F₁  , c = F₂  and  ∠A = ∠x

Given that F₁ = 100 pounds  , F₂ = 150 pounds  and  ∠x = 180° - 40° = 140°

∴ (Resultant force)² = 100² + 150² - 2 * 100 * 150 * cos (∠140) = 55481

∴ Resultant force = √55481 = 235.54 ≅ 236 pounds

The answer is option 4 ⇒ 236 lb.