A 38000-Mg ocean liner has an initial velocity of 4 km/h. Neglecting the frictional resistance of the water, determine the time required to bring the liner to rest by using a single tugboat which exerts a constant force of 195 kN. The time required is min ___ s.

216.59 s.

Explanation:

Using,

F = ma Equation 1

Where F = force exerted by the tugboat, m = mass of the ocean liner, a = acceleration of the ocean liner

make a the subject of the equation

a = F/m Equation 2

Given: F = 195 kN = 195000 N, m = 38000 Mg = 38000000 kg.

Substitute into equation 2

a = 195000/38000000

a = 5.13×10⁻³ m/s²

Also using,

Assuming the liner is decelerating

a = (u-v)/t Equation 3

Where v = final velocity, u = initial velocity, t = time

make t the subject of the equation

t = (u-v)/a Equation 4

Given: u = 4 km/h = 4(1000/3600) = 1.111 m/s, v = 0 m/s, a = 0.00513 m/s²

Substitute into equation 4

t = (1.111-0)/0.00513

t = 216.59 s.

wavelength divides in half and speed stays the same.

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