Question

A 500,000 kg cargo ship is traveling at 75 km/h when its engine is shut off. The magnitude of the frictional force between boat and water is proportional to the speed v of the boat: f k = 85v, where v is in meters per second and f k is in newtons. Find the time in hours for the ship to slow to one-third of its original speed because of the friction with the water.

Answer 1

Answer:1.8 hr

Step-by-step explanation:

Given

mass of cargo=500,000 kg

initial speed
`=75 km/h\approx 20.833 m/s`

Frictional force=85 v

at t=0 engine is shut off so acquired speed is slowly decreasing

`85v=-500,000\frac{\mathrm{d} v}{\mathrm{d} t}`

`85dt=-(dv)/(v)`

Integrating both sides

`85\int_(0)^(t)dt=-500,000\int_(20.83)^(6.944)(dv)/(v)`

`85t=500,000\ln (1)/(3)`

t=6462.425 s

t=1.8 hr