59.

(a) If the skier covers a distance L during time t with zero initial speed and a constant acceleration a,

then L = at

2

/2, which gives the acceleration a

1

for the first (old) pair of skis:

a

1

=

2L

t

2

1

=

2(200 m)

(61 s)

2

= 0.11 m/s

2

and the acceleration a

2

for the second (new) pair:

a

2

=

2L

t

2

2

=

2(200 m)

(42 s)

2

= 0.23 m/s

2

.

(b) The net force along the slope acting on the skier of mass m is

F

net

= mg sin θ

− f

k

= mg(sin θ

− µ

k

cos θ) = ma

which we solve for µ

k1

for the first pair of skis:

µ

k1

= tan θ

−

a

1

g cos θ

= tan 3.0

◦

−

0.11

9.8 cos 3.0

◦

= 0.041

and µ

k2

for the second pair:

µ

k2

= tan θ

−

a

2

g cos θ

= tan 3.0

◦

−

0.23

9.8 cos 3.0

◦

= 0.029 .