A ski slope drops at an angle of 24 degrees with respect to the horizontal and is 500 m long. A 60 kg skier skis down from the top to the bottom of the slope.

A.) Determine the change in gravitational potential energy of the skier+earth system.
b.) If 20% of the gravitation potential energy of the system is transformed into the kinetic energy of the skier, how fast is the skier going at the bottom of the slope?

gwapa ko

To determine the change in gravitational potential energy of the skier+earth system, we need to first calculate the initial and final potential energies.

a) Change in gravitational potential energy:

The gravitational potential energy formula is given by:
PE = m * g * h

where PE is the potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the change in height.

The change in height can be determined using the length of the slope and the angle of the slope with respect to the horizontal. Since the slope forms a right-angled triangle with the ground, we can use trigonometry to find the height (h).

Using trigonometry, we can determine:

sin(24 degrees) = h / 500 m

Rearranging the equation, we find:
h = sin(24 degrees) * 500 m

Now we can calculate the initial and final potential energies:

Initial potential energy (at the top of the slope):
PE_initial = m * g * h_initial

Final potential energy (at the bottom of the slope):
PE_final = m * g * h_final

The change in gravitational potential energy is given by:
ΔPE = PE_final - PE_initial

where ΔPE represents the change in potential energy.

b) To determine the speed of the skier at the bottom of the slope, we can use the information that 20% of the gravitational potential energy is transformed into kinetic energy.

The kinetic energy formula is given by:
KE = 1/2 * m * v^2

where KE is the kinetic energy and v is the velocity of the object.

If 20% of the potential energy is transformed into kinetic energy, then the equation becomes:
KE = 0.2 * ΔPE

Setting this equation equal to the kinetic energy formula, we have:
0.2 * ΔPE = 1/2 * m * v^2

Rearranging the equation, we can solve for the velocity:
v = √((2 * 0.2 * ΔPE) / m)

By substituting the value of ΔPE calculated in part (a) and the mass of the skier (given as 60 kg), we can calculate the velocity.