How Do You Calculate Initial Speed on a Frictionless Incline?

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To calculate the initial speed of a sled on a frictionless incline, energy conservation principles are applied. At the bottom of the slope, the sled possesses kinetic energy, while at the maximum height, it has gravitational potential energy. The sled does not lose energy while moving up the slope, meaning the initial kinetic energy equals the potential energy at the peak height. By equating these energies, the initial speed can be determined using the height gained and the incline angle. This approach effectively demonstrates the relationship between kinetic and potential energy in a frictionless system.
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Please can someone explain to me how to get the answer to this problem:

A sled is initially given a shove up a frictionless 27.0° incline. It reaches a maximum vertical height 1.20 m higher than where it started. What was its initial speed?

Thank you.
 
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the easiest way would be using energy conservation

at the bottom of the slope what kind of energy does the cart have?

at the top of the slope what kind of energy does the cart have?

can you calculate either of these energies?







Did the cart lose any energy on its up the slope? It it didnt waht can you say about the two energies you just calculated?
 

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