Two tugboats are towing a ship. Each exerts a force of 6 tons, and the angle between the towropes is 60°. what is the resultant force on the ship?

Question

asked May 28, 2023 121k views

1 Answer

Pjozsef · Answer 1 · 2023-06-03T07:56:26+0000

10.39tons

The force exerted on the two tugboats F1 = F2 = 6tons

According to the cosine rule;

$R^2=F_1^2+F_2^2+2F_1F_2cos\theta$

where

R is the resultant force

theta is the angle between the two ropes

Substitute the given parameters

$\begin{gathered} R^2=6^2+6^2+2(6)(6)cos60^0 \\ R^2=72+72cos60^0 \\ R^2=72+72(0.5) \\ R^2=72+36 \\ R^2=108 \\ R=√(108) \\ R=10.39tons \end{gathered}$

Therefore the resultant force on the ship is 10.39tons