I saw this picture on one of my social media sites with the caption, "I'd do this in a heart beat! Who's with me!"
I was about to go balls to the walls and say, "I'm in! When and where??" But then I got to thinking, how fast would I be going when I hit the water? If I were going too fast, would it hurt me?
SO I was trying to figure this out, and I'm not very good at physics so I was wondering if you guys could help me out.
I estimate the guy is 90 kg in mass, the wire is angled pi/6 from the horizontal and he's about 50 meters above the water when he starts (all estimates...).
What is the formulas I need to figure out the speed the guy will be going once he hits the water? I know there's some calculus in there, and I'm pretty good at calculus.
Answer
The only force which works is gravity1. So, change in gravitational potential energy equals final Kinetic energy(assume initial is zero). mgh=mv2/2
here h is vertical height traversed.See the velocity does not depend on angle of string, mass of body too..
Let's see the kinematics of body.
The length of string is hcosecθ (θ being angle with horizontal assumed π/6)
acceleration of body along the string=gsinθ
Now using:v2=u2+2as
v2=0+2×hcosecθ×gsinθ
Working in differentials
for v along the rope. dv/dt=vdvdx=a
1)Assuming the pulley being used to slide to be friction less.Though not possible.Also the rope is assumed to be in-extensible and straight.
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