Light, dry snow is called powder. Skiing on a powder day is different than skiing on a day when the snow is wet and heavy. When you slow down on dry snow the maximum (negative) acceleration caused by the snow acting on your skis is about two-fifths as much as that of stopping on wet snow. For a given initial velocity, how does the time td td it takes to stop on dry snow differ from the time tw it takes to stop on wet snow?

Given:

- Acceleration a_dry = 0.4*a_wet

- initial velocity V_i

Find:

By how much does time taken to stop of dry snow differ from time taken to stop on wet snow?

Solution:

- Time taken to stop on wet snow t_wet:

V_f = V_i + a_wet * t_wet

t_wet = - a_wet / V_i

- Time taken to stop on wet snow t_wet:

V_f = V_i + a_dry * t_dry

t_dry = - a_dry / V_i

- Difference in t_wet and t_dry:

t_dry - t_wet = - a_dry / V_i + a_wet / V_i

dt = (a_wet - a_dry) / V_i

dt = (a_wet - 0.4*a_wet) V_i

dt = 0.6*a_wet / V_i