When moving to a new apartment, you rent a truck and create a ramp with a 244 cm long piece of plywood. The top of the moving ramp lies on the edge of the truck bed at a height of 115 cm. You load your textbooks into a wooden box at the bottom of the ramp (the coefficient of kinetic friction between the box and ramp is = 0.2). Then you and a few friends give the box a quick push and it starts to slide up the ramp. A) What angle is made by the ramp and the ground?B) Unfortunately, after letting go, the box only tables 80cm up the ramp before it starts coming back down! What speed was the box initially traveling with just after you stopped pushing it?

A)    θ = 28.1º , B)         v = 2.47 m / s

Explanation:

A) The angle of the ramp can be found using trigonometry

         sin θ = y / L

         Φ = sin⁻¹ y / L

         θ = sin⁻¹ (115/244)

         θ = 28.1º

B) For this pate we can use the relationship between work and kinetic energy

       W =ΔK

where the work is

       W = -fr x

the negative sign is due to the fact that the friction force closes against the movement

Lavariacion of energy cineta is

         ΔEm = ½ m v² - mgh

        -fr x = ½ m v² - m gh

the friction force has the equation

         fr = very N

at the highest part there is no speed and we take the origin from the lowest part of the ramp

To find the friction force we use Newton's second law. Where one axis is parallel to the ramp and the other is perpendicular

Axis y . perpendicular

            N- Wy = 0

            cos tea = Wy / W

            Wy = W cos treaa

             N = mg cos tea

we substitute

- (very mg cos tea) x = ½ m v²2 - mgh

            v2 = m (gh- very g cos tea x)

   let's calculate

           v = Ra (9.8 0.80 - 0.2 9.8 0.0 cos 28.1)

           v = RA (7.84 -1.729)

           v = 2.47 m / s

note: the given question is incomplete.

complete question is given below.

which is an example of kinetic energy?

a. the energy stored in ethanol  

b. a hockey puck sliding across the ice  

c. a compressed spring  

d. a ball sitting at the top of a ramp

solution: the kinetic energy is the energy posses by the virtue of the motion of the object.

in the given options, a, c and d are the example of potential energy because it is the energy posses by the virtue of the rest of the object. but option b has the kinetic energy as the object is in motion.

hence, a hockey puck sliding across the ice   is the apex example of kinetic energy.

so, the option (b) a hockey puck sliding across the ice   is the correct option.