Question

Two tugboats pull a larger boat with forces of 25,000 N on each tow rope. What is the resultant force on the ship if the angle between the two ropes is 40°?

Answer 1

Given below the arrangement of loading on the larger boat by two tug boats.

F₁ = 25000 N

F₂ = 25000 N

Angle between them θ = 40⁰

Resultant between two vectors,
`F=√(F_1^2+F_2^2+2F_1F_2cos\theta )`

Substituting

`F = √(25000^2+25000^2+2*25000*25000*cos 40) \\ \\ =46984.63N\\ \\ =46.98 kN`