Answer
a) uphill
b) $\Delta y=3.65m$
Work Step by Step
(a) We know that the skater has gone uphill since the work done by the skater is greater than that of friction, which means that the skater has gained mechanical energy. On the other hand, the final speed of the skater is less than the initial speed, which shows us that he lost kinetic energy but gained potential energy.
(b) We can find the change in height as
$\Delta y=\frac{W_{nc1}+W_{nc2}-\frac{1}{2}(v_f^2-v_i^2)}{mg}$
We plug in the known values to obtain:
$\Delta y=\frac{3420+(-715)-\frac{1}{2}(81.0)[(1.22)^2-(2.50)^2]}{(81.0)(9.81)}$
$\Delta y=3.65m$
