Timandm

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Comic Book Jumping - The Sonic Boom that never was...

So, I've been saying I'd write a blog about the physics involved in comic book jumping.  After many calculations, and double checking, I've decided to omit the equations unless someone REALLY wants to see them.    If you feel my numbers are wrong here, then by all means, have them checked.  I've asked a friend to verify my calculations (and he MUCH better at physics that I am.)
 
So, I once posed the following question to students in a freshmen physics class. 
 Can the Incredible Hulk jump ten miles without causing a sonic boom? 

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Although that was a while back, I suspect some of them are still trying to figure that out...  But I'm going to give you the answer.   And the answer is... Not only no, but SMURF NO!
 
To jump a distance of 10 miles, the Hulk would need to jump:
  • at an angle of 45 degrees
  • with an initial velocity of 890 mph
  • reaching a maximum height of 4.38 miles
  • with a total flight time of about 57 seconds
 So, the Hulk has to break the sound barrier in order to leap a distance of ten miles.  Now, he will slow down as he approaches the masimum height, but he is going to speed back up as he plummets to earth, and he WILL impact with the same speed at which he launched.  So, he will ALSO break the sound barrier as he comes in for a landing.  Thus, to leap a distance of ten miles, the Incredible Hulk must create TWO SONIC BOOMS...
 
If the Hulk launches at any angle OTHER than 45 degrees, he will have to leap even faster to make ten miles.
 
Now, a jumper is basically a projectile.  A projectile, by definition, is any object in motion acted  upon by ONLY one force.  In this case, that force is gravity.
A simpler definition would be, any object that has been launched/hurled/projected into the air...  
 
An arrow from a bow.  A bullet from a gun.  A ball from a cannon.  These are all projectiles,  something launches them, but once they are in motion, only gravity is acting on them.  Well, anything that jumps is basically a projectile.  The springing is what gives the jumper their initial velocity, but once their feet leave the ground, gravity is the ONLY force acting on them.  (We are ignoring air resistance.)
 
So, when the Hulk or Spider-man or Squirrel girl leap, they are projectiles.  The higher or further something leaps, the faster their initial velocity (speed) must be. 
Now, according to Marvel's wiki-page on the Hulk, he usually jumps about 3 miles, but has been known to jump 1000 miles with a single jump... Um... yeah...
 
A 3 mile jump requires the Hulk to jump:   
  • at an angle of 45 degrees
  • with an initial velocity of 490 mph
  • reaching a maximum height of 1.3 miles
  • with a total flight time of about 31 seconds
 A 1000 mile jump requires the Hulk to jump:   
  • at an angle of 45 degrees
  • with an initial velocity of 8900 mph
  • reaching a maximum height of 439 miles
  • with a total flight time of 9.6 minutes
 8900 mph is MACH 12.7.   He has to launch at about 13 times the speed of sound?!?!    That's roughly half the speed of the space shuttle when it launches...  But, it's the comic book universe so.....
 
Anyway, now you know....
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