Respuesta :
The velocity when the cable becomes taut can be obtained by assuming
that the tugboat collides with a barge moving in the same direction.
Response (approximate value):
- The velocity of the tugboat after the cable becomes taut is: 5.824 ft./s.
How is the law of conservation of linear momentum used to calculate the speed of the tugboat?
Weight of the tugboat, m₁ = 240–ton
Speed of the tugboat, v₁ = 6 ft./s
Weight of the barge, m₂ = 100–ton
Rate at which the towing cable is being unwound, v₂ = 5.4 ft./s
Required:
Velocity of the tugboat after the cable becomes taut.
Solution:
m₁ = 240 ton = 240,000 kg
m₂ = 100 ton = 100,000 kg
The velocity of the barge at rest is assumed to be the rate at which the cable is being unwound, and in the direction of the tugboat.
According to the law of conservation of linear momentum, we have;
m₁ × v₁ + m₂ × v₂ = (m₁ + m₂) × v₃
Which gives;
240 × 6 + 100 × 5.4 = (240 + 100) × v₃
1980 = 340 × v₃
Which gives;
[tex]v_3 = \dfrac{1980}{340} = \dfrac{99}{17} = 5\frac{14}{17} \approx \mathbf{ 5.824}[/tex]
The velocity of the tugboat after the rope becomes taut is 5.824 ft./s
Learn more about the law of conservation of linear momentum here:
https://brainly.com/question/4388270
