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A cruise ship with a mass of 1.03 ✕ 107 kg strikes a pier at a speed of 0.752 m/s. It comes to rest after traveling 6.94 m, damaging the ship, the pier, and the tugboat captain's finances. Calculate the average force (in N) exerted on the pier using the concept of impulse. (Hint: First calculate the time it took to bring the ship to rest, assuming a constant force. Indicate the direction with the sign of your answer.)

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Answer:

419815.72 N

Explanation:

F = Force

t = Time

Average speed

[tex]v_{av}=\frac{0.752+0}{2}\\\Rightarrow v_{av}=0.376\ m/s[/tex]

Time = Distance / Speed

[tex]\text{Time}=\frac{6.94}{0.376}\\\Rightarrow \text{Time}=18.45\ s[/tex]

Impulse

[tex]J=m\Delta v\\\Rightarrow Ft=m\Delta v\\\Rightarrow F=\frac{m\Delta v}{t}\\\Rightarrow F=\frac{1.03\times 10^7\times (0-0.752)}{18.45}\\\Rightarrow F=-419815.72\ N[/tex]

The force exerted on the pier is 419815.72 N

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