# Find the time required for the boat to slow to 45 km/hr

hey

A 1000 kg boat is travelling at 90km/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: force of kinetic fricition=70v, where v is in meters per second and the force is in newtons. Find the time required for the boat to slow to 45 km/hr

## Answers and Replies

dextercioby
Science Advisor
Homework Helper
king_naeem said:
hey

A 1000 kg boat is travelling at 90km/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: force of kinetic fricition=70v, where v is in meters per second and the force is in newtons. Find the time required for the boat to slow to 45 km/hr

I'm a theorist,so i'll let u plug the numbers:
The Newton's law states:$m\frac{dv}{dt}=-\alpha v$,where alpha is that 70 in your problem:
Integrate the ODE wrt to proper limits:
Final result:$t=(\frac{1000}{70}\ln 2) s$

Good luck!!