having a hard time with these efficiency question, help on any of them is appreciated! can use kinematics, dynamics and energy equations.

Question

An amusement park has a slide for which participants are given a cloth sack to sit on. Riders start from rest at the top of the slide, which is 6.00 m high. Assuming that 80.0% of the gravitational potential energy is "lost" to friction during the slide, how fast will a 30.0 kg child be travelling at the bottom of the slide. 

During his job at McDonald's, a student is asked to lift boxes of frozen burgers (mass = 6.00 kg) from the ground to a shelf in the freezer, 2.50 m above the ground. The ingenious student decides that instead of lifting the boxes straight upward, he can use a ramp and slide them up to the shelf. The ramp is 5.10 m long and in order to push the boxes at a constant velocity, he must push parallel to the ramp with a constant force of 55.5 N. What is the % efficiency of the ramp? 

A boy exerts a force of 225 N on a lever to raise a 1250 N rock a distance of 0.13 m. If the efficiency of the lever is 88.7%, how far did the boy move his end of the lever? 

A 125 g ball is thrown with a force of 8.50 N that acts through a distance of 78.0 cm. The ball’s velocity just before it is caught is 9.84 m/s. What percentage of the energy transferred to the ball was lost to the atmosphere during flight? 

A raindrop reaches terminal velocity very quickly as it falls to Earth due to the work friction does during the descent. If a 0.500 g raindrop formed 1.50 km above the Earth reaches the ground with a speed of 5.20 m/s, what is the percentage of energy that is lost due to work done by friction? 

Answer 1

An amusement park has a slide for which participants are given a cloth sack to sit on. Riders start from rest at the top of the slide, which is 6.00 m high. Assuming that 80.0% of the gravitational potential energy is "lost" to friction during the slide, how fast will a 30.0 kg child be travelling at the bottom of the slide. 

potential energy at height h= mgh = 30*9.8*6= 1764 J

as 80% is lost remaing = 20%

So 20% of 1764 J = 0.2*1764=352.8J

Which will be Kinetic energy at the bottom= 1/2mv² = (1/2)30*v²

15V² = 352.8

V² = 352.8/15

Get V ( m/s)