AAMC 5 Question #43

[kabtq9s]

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Guys,

I have read some explanations of this problem but I'm still confused. Can some one please explain it as simply as possible. Also why do we have to write the potential energy to be equal to the kinetic energy in the first place.

http://mysowar.files.wordpress.com/2011/05/43.jpg

Thanks in advance

 

[Rabolisk]

The explanation given is pretty good, so it's hard to give a simpler one. The loss in potential energy is equal to the gain in kinetic energy because the only force present is the gravitational force. Gravity is a conservative force, so total mechanical energy (gravitational potential energy + kinetic energy) must be conserved.

 

[kabtq9s]

The explanation given is pretty good, so it's hard to give a simpler one. The loss in potential energy is equal to the gain in kinetic energy because the only force present is the gravitational force. Gravity is a conservative force, so total mechanical energy (gravitational potential energy + kinetic energy) must be conserved.

Its just hard for me to intuitively come up with the methodology they used to solve this question. What comes intuitively to me (since the question is asking for speed) is to compare (or get the ratio of) the final velocity of the 20m sled with that of the 10m sled using an equation v=sqt(2gh) that I memorized previously from here. This gives me sqt2/2. But I'm not sure if I was just lucky or is that really another correct way of solving the problem.

Thanks in advance

 

[mgpenguin]

The way I did this problem was to solve for v in mgh = 1/2 mv^2. So I got the answer v = sqrt(2gh). So I figured then that since v is proportional to the sqrt(h), plugging in sqrt(h/2) reduces the velocity by a factor of sqrt2. For me that seems more intuitive than doing ratios.

 

[Rabolisk]

Its just hard for me to intuitively come up with the methodology they used to solve this question. What comes intuitively to me (since the question is asking for speed) is to compare (or get the ratio of) the final velocity of the 20m sled with that of the 10m sled using an equation v=sqt(2gh) that I memorized previously from here. This gives me sqt2/2. But I'm not sure if I was just lucky or is that really another correct way of solving the problem.

Thanks in advance

You memorized the equation without understanding why?