Question

a) A cruise ship with a mass of 1.00×107 kg strikes a pier at a speed of 0.750 m/s. It comes to rest 6.00 m later, damaging the ship, the pier, and the tugboat captain’s finances. Calculate the average force exerted on the pier using the concept of impulse. (Hint: First calculate the time it took to bring the ship to rest.)

b) The force of the water sloshing near the pier is enough to push the ship back. After it has gone the 6.00 m necessary to reach zero velocity, the water then pushes the ship backward to a velocity of 0.200 m/s over a distance of 1.50m. What is the impulse of the water on the ship?

Answer 1

here,

a)

the mass of ship , m = 1 * 10^7 kg

initial speed , u = 0.75 m/s

s = 6 m

let the time taken to come to rest be t and acceleration be a

using third equation of motion

0^2 - 0.75^2 = 2 * 6 * a

a = - 0.0469 m/s

using first equation of motion

v = u +a * t

0 = 0.75 - 0.0469 * t

t = 16 s

the average force , F = impulse /time

F = - 1 * 10^7 * 0.75 /16 N = - 4.69 * 10^5 N

b)

final velocity ,v = 0.2 m/s

the impulse delevired by the water of on ship , I = m * v

I = 0.2 * 1 * 10^7 kg.m/s

I = 2 * 10^6 kg.m/s