Question

A snowboarder starts from rest on an inclined planar snow surface and gives herself a tiny push to start sliding down the hill. The coefficient of kinetic friction between her snowboard and the snow is 0.14. She notices that she travels 27.81 m horizontally and 39.78 m vertically (downward) before whizzing by a marker flag. How fast is she traveling as she passes the flag?

Answer 1

v = 26.52 m/s

Step-by-step explanation:

Here we know that as she passes the flag she will gain some speed

so here we can say that

Work done by all forces = change in kinetic energy of the system

so we will have

`W_g + W_f = (1)/(2)mv_f^2 - (1)/(2)mv_i^2`

here we know that

`W_g = mgh`

`W_f = -\mu mg d`

`v_i = 0`

h = 39.78 m

d = 27.81 m

so we have

`mgh - \mu mg d = (1)/(2)mv^2 - 0`

`(9.8)(39.78 - (0.14)(27.81)) = (1)/(2) v^2`

`v = 26.52 m/s`