Question

A 1020 kg boat is traveling at 110 km/h when its engine is shut off. The magnitude of the frictional force k between boat and water is proportional to the speed v of the boat. Thus, fk = 75v, where v is in meters per second and fk is in newtons. Find the time required for the boat to slow down to 55 km/h.

Answer 1

Answer: 94 seconds

Step-by-step explanation:

An exact solution will require calculus, since the acceleration is not constant.


M*dV/dt = -fk = -75V
dV/V = -(75/M)dt



Since you have separated variables to opposite sides, the differential equation is easily integrated. 



Therefore,

V2/V1 = -ln2 = (-75/M)T
where T is the time interval.



Then we have that,

T= (M/75)*ln2 = (1020/75)*0.693
= 94 seconds