A skier is gliding along at 5.0{\rm m/s} on horizontal, frictionless snow. He suddenly starts down a 15{\rm ^{\circ}} incline. His speed at the bottom is 15{\rm m/s} .
There is no question here, and the meaning of your {\Rm and ^{\circ}} symbols is unclear
To find the distance covered by the skier on the incline, we can use the concept of conservation of mechanical energy. The total mechanical energy of the skier remains constant throughout the motion.
The mechanical energy of the skier consists of two parts: the kinetic energy (KE) and the potential energy (PE). Initially, when the skier is on the horizontal snow, there is no change in the potential energy as there is no vertical displacement. So, the total mechanical energy is only the kinetic energy at that point.
At the bottom of the incline, the skier reaches a speed of 15 m/s. Here, there is no potential energy (as the skier is at the ground level), so the total mechanical energy is just the kinetic energy at this point.
Since the total mechanical energy is conserved, we can equate the initial kinetic energy to the final kinetic energy:
KE_initial = KE_final
The initial kinetic energy can be found using the formula:
KE_initial = (1/2)mv^2
Where m is the mass of the skier and v is the initial velocity (5.0 m/s).
Similarly, the final kinetic energy can be found using the formula:
KE_final = (1/2)mv^2
Where v is the final velocity (15 m/s).
By equating the initial and final kinetic energies, we can solve for the mass of the skier:
(1/2)m(5.0^2) = (1/2)m(15^2)
Simplifying the equation, we get:
25m = 225m
Dividing both sides by m (assuming m is not zero), we get:
25 = 225
This equation is not true, which means there is an error in the problem statement or the calculations. Please recheck the given information and try again.