30kg的重物以20m/s的初速(沒有外力協助)爬上角度為20的理想平滑山坡.1)以其失去動能=其獲得的位能後計算其爬上山坡的長度.2)以v^2-u^2=2as直接計算長度. (1)和(2)的結果哪個準確?

Both methods give the same answer. In fact, the equation v^2 - u^2 = 2a.s comes from the conservation of mechanical energy.

From conservation of energy, loss of kinetic energy = gain in potential energy
i.e. (1/2)m.u^2 - (1/2)mv^2 = mgh
[where m is the mass of the object, g is th acceleration due to gravity, and h is the vertical height reached].

But h/s = sin(20)
i.e. h = s.sin(20)

Thus, we have, (1/2).u^2 - (1/2).v^2 = g.s.sin(20)
or v^2 - u^2 = -2.[g.sin(20)].s
i.e. v^2 - u^2 = 2.a.s where a = -g.sin(20) is the deceration of the object on the smooth slope.