Ah, the problem is the interpretation of the question.
I think the problem was intended to mean that he starts traveling horizontally (at the bottom of the hill) when he enters the snow.
I'm pretty sure that your professor does want you to find what the relative uncertainty is (which is Δp/p).
The key to this problem is that Δx depends on p.
The wavefunction of a particle must satisfy the following condition:
\int_{-\infty}^{\infty} |\Psi|^2 dx = 1
Basically, this means that the total probability of finding the particle anywhere is one. It doesn't really make sense otherwise.
If you were to increase the amplitude of the...