Problem D: Bungee Jumping
Once again, James Bond is fleeing from some evil people who want to see
him dead. Fortunately, he has left a
bungee rope on a nearby highway bridge which he can use to escape from his
enemies. His plan is to attach one end of the rope to the bridge, the other end of
the rope to his body and jump off the
bridge. At the moment he reaches the ground, he will cut the rope, jump
into his car and be gone.
Unfortunately, he had not had enough time to calculate whether the bungee
rope has the right length, so it is not clear at all what is going to
happen when he jumps off the bridge. There are three possible scenarios:
- The rope is too short
(or too strong), and James Bond will
never reach the ground.
- The rope is too long
(or too weak), and James Bond will be
going too fast when he touches the
ground. Even for a special agent, this
can be very dangerous. You may assume
that if he collides at a speed of more
than 10 m/s, he will not survive the
impact.
- The rope's length and
strength are good. James Bond touches
the ground at a comfortable speed and
can escape.
As his employer, you would like to know whether James Bond survives
or whether you should place a job ad for the soon-to-be vacant position
in the local newspaper. Your physicists claim that:
- The force with which
James is pulled towards the earth is
9.81 * w,
where w is his weight in
kilograms and 9.81 is the Earth
acceleration in meters over squared
seconds.
- Mr. Bond falls freely
until the rope tautens. Then the
force with which the bungee rope pulls
him back into the sky depends on the
current length of the rope and is
k * Δl,
where Δl is the
difference between the rope's current
length and its nominal, unexpanded
length, and k is a
rope-specific constant.
Given the rope's strength k, the nominal length
of the rope l in meters, the height of the
bridge s in meters, and James Bond's body
weight w, you have to determine what is going
to happen to our hero. For all your calculations, you
may assume that James Bond is a point at the end of
the rope and the rope has no mass. You may further
assume that k, l, s, and w
are non-negative and that s < 200.
The input contains several test cases, one test case per line. Each test
case consists of four floating-point numbers (k, l, s,
and w) that describe the situation. Depending on what is going to
happen, your program must print "Stuck in the air.",
"Killed by the impact.", or
"James Bond survives.".
Input is terminated by a line containing four 0s, this line
should not be processed.
Sample Input
350 20 30 75
375 20 30 75
400 20 30 75
425 20 30 75
450 20 30 75
400 20 30 50
400 20 30 80
400 20 30 85
0 0 0 0
Output for Sample Input
Killed by the impact.
James Bond survives.
James Bond survives.
James Bond survives.
Stuck in the air.
Stuck in the air.
James Bond survives.
Killed by the impact.
Stefan Büttcher