please help.....

 If v is the initial velocity, then the velocity after it comes out of first plank is 0.10v.

Initial KE = mv²/2 and Final KE = 0.01mv²/2.

The loss in KE as it passes through one plank = Initial KE - Final KE = 0.99mv²/2.

So the loss of KE if we use n plank's is, = n(0.99mv²/2).

and this total loss has to be equal to initial KE, if we have to stop it.

Hence n(0.99mv²/2) = mv²/2,

which gives n = 1.01, hence 2 planks will be required.

regards,

Team,

TopperLearning.