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 .