A skier (whose mass is 60 kg) skis down a smooth (frictionless) ski slope, as sh

Question

A skier (whose mass is 60 kg) skis down a smooth (frictionless) ski slope, as shown in the diagram (***Just has a picture showing a stair-case like slope with 30 m being the highest, 10 m being the next highest, and 0 m of absolute bottom of slope***). The skier pushes off at the top with a speed of 1.5 m/s. If we define the absolute bottom of the slope to have 0 gravitational potential energy, (1) what is the gravitational potential energy (in J) when she is at the top of slope (just before she pushes off)? (2) What is the kinetic energy of the skier (in J) when she reaches a middle flat area 10 m higher in altitude than the absolute of the slope? (3) What is the kinetic energy of the skier (in J) when she reaches the absolute bottom of the slope?

Explanation / Answer

1) Gravitational PE at top of slope = m * g * h = 60 * 9.8 * 30 = 17640 J

2) Her loss of PE must be what is converted to KE. At the 10 m level,

her PE = m * g * 10 = 5880 J

The loss of PE is = 17640 - 5880 = 11760 J
So her KE = 11760 J

3) At the bottom of the slope, all of the PE she had at the top must have been converted to KE at the bottom. So,
KE at the bottom = 17640 J

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