Repost: Can Spiderman Make It?

Question

Spiderman discovers a ticking bomb in a warehouse, with exactly 1 second left on it. He needs to escape from the warehouse before it blows up. The wall is 9 meters from him, is 20 meters high, and the open skylight in the ceiling is 10 meters from the wall. Spiderman is capable of accelerating at 72 meters/second² on the ground, wall, or ceiling, as well as leaping from either the ground to wall, or wall to ceiling, or ground to ceiling, or any combination. However, during a leap, he travels in a straight line only as fast as he was running at the time of the takeoff. Can he make it in time?

Note that 1) Spiderman takes a full second to achieve a speed of 72 m/sec, and 2) there is no additional implied "boost" upon takeoff on any flight, only the speed he was already travelling on a surface.

Remember, Peter Parker was a science genius, so with his Spidey powers, he's able to think problems like this through in a tiny fraction of a split second! Can you?

He can leap straight to the skylight from anywhere, but his flight speed would only be what his speed would be on any surface before takeoff. I could have made this problem more complicated by allowing a certain boost velocity added to his surface speed, but for this problem, it's 0. For Spiderman to leap directly to the skylight from the bomb in 1 second, he would need a minimum boost speed of 20.025 m/sec.

Foxy Cat, if Spiderman choses to race 39 meters with no leaping, the time it takes to cover it is (1/2)(72)t² = 39, or about t = 1.04083 sec, too late! Too slow!

Mamad, Spiderman can maintain his speed even after any flight, he just needs a surface for traction for further acceleration. Unlike some other superheroes, he does not have rocket propulsion, so he cannot accelerate in air.

falzoon, I've computed your path time to be 1.1418 seconds---close, but no cigar.

Foxy Cat, in 0.3 seconds, Spiderman will have travelled 3.24 meters, so that even if he was going away from the wall, and jumps directly to the skylight, the time required would be 1.07329 seconds. Kaboom, sorry!

Falzoon, I feel for you. But remember, Spiderman is a genious. Are you less than Spiderman?

Answer 1

Spiderman runs and jumps onto the wall at a 45º angle,
when he is approx. 0.860164 metres from the wall. He
then jumps to the skylight. Total time taken is 1 second.
If I find the time to get my head together, I'll elucidate.
If I find the time to realise I am wrong, I'll let you know, if you
don't get in first. Thanks for the great question.

EDIT : I still haven't got my head around this problem yet.
I would like to spend more time on it, but I have another life
somewhere. So far, I've been toying with the equation:
(9-x) / cos(t) + 10 / sin(t) + 2x - 12*sqrt(x) = 0,
which I hope is the correct one, by inserting various values
for t and calculating what x should be. There seem to be an
infinite number of solutions, although some values don't work.
For example, for t = 45º, I get distance from wall of approx.
2.45262 metres as the jumping-off point, but there are all
sorts of other angles that work. Other equations start out
OK, but soon get ludicrously complicated. Am I doing
something wrong? Do I need to use partial derivatives,
which I'm not confident at? Am I on the right track?
Will I still be sane tomorrow?
Wishing for more time as this is a fascinating problem.

EDIT 2 :
I think I have it this time. I found out that my last calculations
would never come to less than about 1.145 seconds. So,
Spiderman runs to the wall, then runs up the wall, anywhere
between approx. 8.721568 metres and 13.46894 metres,
whereupon he jumps to the skylight.
When he at those extreme values, he takes 1 second.
Anywhere between takes less than 1 second.
The equation to solve for those above zeros is:
-9x^2 + 768x^3 - 10048x^2 - 13568x + 425216 = 0
Am I in spidey's league now? Perhaps a little slow maybe,
as the bomb went off days ago.

Answer 2

RE EDITED***WILL SPIDERMAN DIE? EDITION**
(sunday edition: $3.50)

Well you said he needed 1 secong to accelerate to 72m/s
so I assumed, if it would take him 0.1s to get from 0 to 7.2m/s,
so in 0.3s he would have reached 21.6 m/s and
so he would have covered 1 meter to get under the skilight.


I chose 21.6m/s because he had to cover 21 meters since
you mentionned: "However, during a leap, he travels in a straight line only as fast
as he was running at the time of the take off"...
So 21 meters was the fastest route, in this situation.


Also 21.6m/s was his final velocity, he had time to cover 21m
under 1s

21/21.6=0.98s

Duh....I guess you are right, he would have covered 3m...



Maybe the answerer under me might come up with a better alternative...


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Answer 3

We are talking about Spider-man right? He has a power called spider sense and he would never even go inside the warehouse! If you were talking about someone else like Batman or Wolverine then the question would make more sense. You have to factor their powers into the equation too!

Answer 4

Peter Parker's a genius so he might not get out of the ware house but do sumthin bout the bomb itself!

Answer 5

Duh you've got speed and acceleration mixed up
No points for the question

Answer 6

your crazy over spiderman..............."huh" am not at all.