A kid slides down an icy (frictionless) hill starting from res. At the top his gravitational potential energy is 500J. Suppose after reaching the bottom he then continues sliding up another icy slope on the other side of the valley. Whenhe finally comes to a stop he will have reached a height :
A>equal to the height he started from on the other hill
B>less than the height he started from on the other hill
C>more than the height he started from on the other hill
D>none of the above
To determine the height the kid will reach on the other hill after sliding down and coming to a stop, we need to consider the conservation of energy.
At the top of the first hill, the kid has gravitational potential energy (PE) of 500J. As he slides down the hill, this potential energy is converted into kinetic energy (KE).
Since the hill is frictionless, we can assume that no mechanical energy is lost due to friction.
Therefore, at the bottom of the hill, all of the gravitational potential energy (500J) is converted into kinetic energy. We can use the equation:
PE = KE
500J = 1/2 * m * v^2 (where m is the mass of the kid and v is his velocity at the bottom of the hill)
Since we are not given the mass of the kid or his velocity, we cannot determine their exact values. However, we can use this information to answer the question.
When the kid starts sliding up the other hill, his kinetic energy is being converted back into potential energy. The height he reaches on the other hill will depend on how much of the kinetic energy is converted back into potential energy.
Since the other hill is on the other side of the valley, it is at a lower height than the starting height. Therefore, the kid will not reach a height equal to or more than the height he started from on the other hill.
So the correct answer is B) less than the height he started from on the other hill.
To determine the height the kid will reach on the other hill, we need to understand the conservation of mechanical energy. In a frictionless system, mechanical energy is conserved, so at any given point, the total mechanical energy remains constant.
Initially, the kid has only gravitational potential energy at the top of the first hill, which is 500J. As he slides down, this potential energy is converted into kinetic energy. At the bottom of the hill, all the potential energy is converted into kinetic energy, so the total mechanical energy is now 500J (kinetic energy).
When the kid starts moving up the other hill, his kinetic energy starts to decrease - it gets converted back into potential energy. According to the conservation of mechanical energy, the total mechanical energy should remain constant.
Since there is no friction in this scenario, no energy is lost to other factors like heat or sound. Therefore, the total mechanical energy at the top of the second hill should still be 500J.
Given that the kid started with a gravitational potential energy of 500J on the first hill, and the total mechanical energy should remain constant, we can conclude that the height the kid reaches on the other hill will also be equal to the height he started from on the other hill.
Therefore, the answer is option A - equal to the height he started from on the other hill.