Shake Hands With Your Opponent?
A and B are the only two participants of a race. The rules of this race are very different from the normal rules, but are very simple.
(1) A has to run with a constant speed "u"
(2)B will stand "x" meters ahead of A, and will begin from rest moving with a constant acceleration "a"
(3)Whenever A and B meet each other on the track they need to shake hands.
If 'm' is the maximum number of times A and B can shake hands on the track, then find m + 1.
Details
they never waste time or slow down to shake hands. they do it in an instant.
assume that the race track is of infinite length
The answer is 3.
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1 solution
The maximum number of hand shakes is equal to the maximum number of times A and B meet on the track.
Depending on the values of "a", "u", and "x" there are three possibilities
CASE 1
A never overtakes B.
.'. 0 handshakes
CASE 2
A and B meet for an instant, then B again overtakes A.
.'. 1 handshake
CASE 3
A overtakes B, remains ahead of B for sometime, then B overtakes A.
.'. 2 handshakes
maximum number of handshakes is 2.
.'. m + 1 = 3