We know, by conservation of energy :

Therefore,

Putting given values, we get :

Therefore, the spring be compressed to 6.93 cm to send the ball twice as high.
Hence, this is the required solution.
If time is specified, the distance may be estimated in constant acceleration using the formula: X=(at2)/2 if the beginning velocity is 0. (A automobile begins from a stop...) As a result, X=(6*10*10)/2=600/2 = 300 m.
Answer:

Explanation:
According to the law of conservation of linear momentum, the total momentum of both pucks won't be changed regardless of their interaction if no external forces are acting on the system.
Being
and
the masses of pucks a and b respectively, the initial momentum of the system is

Since b is initially at rest

After the collision and being
and
the respective velocities, the total momentum is

Both momentums are equal, thus
Solving for 


The initial kinetic energy can be found as (provided puck b is at rest)


The final kinetic energy is


The change of kinetic energy is
