Conservation of energy and power questions

Question

1.Eric drops a 2.8 kg water balloon that falls a distance of 22 m off the top of a building. What is the kinetic energy at the bottom?

2.Eric drops a 4.3 kg water balloon that falls a distance of 27 m off the top of a building. What is the velocity at the bottom?

3.A roller-coaster goes over an 16 m tall hill then approaches a 20 m hill. What is the minimum velocity the roller-coaster would need when going over the 16 m hill to make it to the top of the 20 m hill?

4.

Jasmine, a San Francisco hot dog vender, has fallen asleep on the job. When an earthquake strikes, her 277 kg hot dog cart rolls down Nob Hill and reaches point A at a speed of 3.5 m/s. How fast is the hot dog cart going at point B when Jasmine finally wakes up?

*answer and explanation please*

Answer 1

1) KE after falling from a height with intial velocity equal zero = mgh = 1/2mv² = 2.8*9.81*22 = 6037 J

2) Velocity = sqrt(2gh) = sqrt(2*9.81*22)= 20.78 m/s

3) Car must minimally have KE at top of 16 m hill = the increase of PE at 20 m hill = sqrt(2g(20-16))= 8.86 m/s.

4) Total Energy at point A = 277*50*g +.5*277*3.5² = 137565 J and will be the same at point B (no friction). Therefore the velocity at B = sqrt(2*TE/277)= 31.5 m/s