A roller coaster has a 100.0 kg cart at the top of a 22.0 m ramp. As it goes down the ramp, it change 800.0 joules of energy to heat due to friction. What will the kinetic energy be at the bottom of the ramp?

a. 800 J
b. 100 J
c. 0 J
d. 20760 J
e. 22360 J

d.20760 J

Explanation:

We are given that

Mass of cart=m=100 kg

At the top,h=22 m

Amount of energy convert into heat due to friction=E=800 J

We have to find the kinetic energy at the bottom of the ramp.

Potential energy drop=mgh=

Kinetic energy at the bottom=Potential energy drop-energy lost due to friction

Kinetic energy at the bottom =(21560-800) J

Kinetic energy at the bottom=20760 J

Hence, the kinetic energy at the bottom of the ramp=20760 J

d.20760 J

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .

the moving of the box is a result of centripetal force. think of that  as a car or a truck in this case creates a turn, the force of friction performing upon the turned wheels of the car runs centripetal force obligatory for circular motion for the things inside it.