A knight moves on a chessboard two squares up, down, left, or right followedby one square in one of the two directions perpendicular to the first part of the move (i. e.,the move is L-shaped). Suppose the knight is on an unbounded board at square (0,0) and wewish to move it to square (x, y) in the smallest number of moves. (For example, to move from(0,0) to (1,1) requires two moves. The knight can move to board locations with negativecoordinates.)

Explanation:

Check attachment for solution.

Generally the movement of the knight is L, i.e (2,1), (1,2),(-1,2),(1,-2) etc.

So using Pythagoras theorem

x^2+y^2=1^2+2^2

x^2+y^2=5

Then, the knight will make one movement when the displacement is √5.

So let take a look at other positions

(1,0),(0,1),(-1,0), (0,-1).

Then, for us to have this kind of movement, the knight has to make 3 movements.

When the displacement is 1, then it will make 3 movement.

Let examine other positions

(2,2) or(-2,-2) or (2,-2) or (-2,2)

When the displacement is √8

Then, the movement of the knight is 4.

Let examine other points

(2,0) or (0,2) or (-2,0) or (0,-2)

When the displacement is 2.

The knight make 2 movement

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.