Question

a 200 kg roller coaster car starts from the top of a 180 m high hill. assume that energy is totally conserved and no energy is lost to friction or air resistance. calculate the velocity of the car when it is 75 m above the ground. what is the speed of the car when it reaches the ground

Answer 1

We just need 3 formula, kinetic, potential and mechanic energy.

Em = Ep + Ek = constant

Em = Ep max = Ek max

Ep max = Ep + Ek

mgh = mxghx + 1/2mv²

200 kg × 10 m/s² × 180 m = 200 kg × 10 m/s² × 75 m + 1/2 × 200 kg × v²

360000 kgm²/s² = 150000 kgm²/s² + 100 kg × v²

360000 - 150000 kgm²/s² = 100 × v²

210000 kgm²/s² = 100 kg × v²

210000/100 kgm²/s² = v²

√2100 m²/s² = v

v ≈ 46 m/s

and when it at the ground the v is

Ep max = Ek max

360000 kgm²/s² = 1/2 mv²

360000 kgm²/s² = 1/2 × 200 kg × v²

360000 kgm²/s² ÷ 100 kg = v²

3600 m²/s² = v²

√3600 m²/s² = v

v = 60 m/s