A tugboat tows a ship with a constant force of magnitude F1. The increase in the ship's speed during a 10 s interval is 5.0 km/h. When a second tugboat applies an additional constant force of magnitude F2 in the same direction, the speed increases by 19 km/h during a 10 s interval. How do the magnitudes of F1 and F2 compare? (Neglect the effects of water resistance and air resistance.)

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Question:

A tugboat tows a ship with a constant force of magnitude F1. The increase in the ship's speed during a 10 s interval is 5.0 km/h. When a second tugboat applies an additional constant force of magnitude F2 in the same direction, the speed increases by 19 km/h during a 10 s interval. How do the magnitudes of F1 and F2 compare? (Neglect the effects of water resistance and air resistance.)

Answers

Answergiven,time  = 10 sship's speed = 5 Km/h F = m a a is the acceleration and m is mass.In the first case F₁=m x a₁where a₁ =  difference in velocity / timeF₁ is constant acceleration is also a constant.Δv₁ = 5 x 0.278Δv₁ = 1.39 m/s[tex]a_1=\dfrac{1.39}{10}[/tex]a₁ = 0.139 m/s²F₂ =m x a₂F₃ = F₂ + F₁Δv₃ = 19 x 0.278Δv₃ = 5.282 m/sa₃=Δv₂ / t[tex]a_3=\dfrac{5.282}{10}[/tex]a₃ = 0.5282 m²/sm a₃=m a₁ + m a₂a₃ = a₂ + a₁0.5282 = a₂ + 0.139a₂=0.3892 m²/sF₂ = m x 0.3892...........(1)F₁ = m x 0.139...............(2)F₂/F₁ratio = [tex]\dfrac{0.3892}{0.139}[/tex]ratio = 2.8

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