31. We denote the magnitude of the frictional force αv, where α = 70 N

· s/m. We take the direction of the

boat’s motion to be positive. Newton’s second law gives

−αv = m

dv

dt

.

Thus,

v

v

0

dv

v

=

−

α

m

t

0

dt

where v

0

is the velocity at time zero and v is the velocity at time t. The integrals are evaluated with

the result

ln

v

v

0

=

−

αt

m

.

We take v = v

0

/2 and solve for time:

t =

m

α

ln 2 =

1000 kg

70 N

· s/m

ln 2 = 9.9 s .