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?

Question

Physics

Sheldon Butler

6 February, 08:45

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?

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Answers (1)

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Salvador Nicholson · Answer 1

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