The Fall

The greatest man I have ever known passed away today. I had to watch the horrible suicide of consulting detective Sherlock Holmes. I feel like the only way to come to terms with his death and respect my genius friend is to understand the science of his death. Or at least that's what my therapist claims. Sherlock was 1.828 8 meters tall and weighed about 71.66759446 kg. The four story building he fell from was 13.716 meters tall and gravity effects falling objects at 9.81 m/s². So how fast was he falling and how long did it take?

Final vertical velocity given vertical displacement: vf² = vyi² + 2g(xi-xf)

vyi²=0m/s  2g=19.6m/s²  xi=13.716m  xf=0m  vf² = 0 + 19.6(13.716-0)

This means that in a perfect system, meaning no air resistance, Sherlock would have been falling at 16.4m/s at the time of impact.

Final vertical velocity given time: vyf = vyi + gt

vyf =16.4m/s vyi=0m/s g=9.81 m/s² t=?  16.4 = 0 + 9.81t

This means Sherlock's fall would have taken 1.67s in a perfect system.

How much kinetic energy did Sherlock have on impact? mgh=GPE 

m=71.66759446kg g=9.81m/s² h=13.716m  (71.6675944)(9.81)(13.716) = 9640J

Because GPE=KE, Sherlock's kinetic energy was also 9640J.

That fall would have killed anyone, so how is Sherlock still alive?

Smashing the Glass

Today our nemesis Moriarty pulled off his biggest stunt to date. He simultaneously broke into the Bank of England, Pentoville Prison, and the Tower of London. I want to focus on the main heist at the Tower of London. All the reports are telling me that Moriarty attached a diamond to the 2 inch thick glass casing surrounding the Crown Jewels using a bit of chewed bubble gum. It is said that Moriarty then took the room's fire extinguisher and hit the diamond, smashing the glass. But this is implausible due to the nature of the glass. Like in the old spy movies, diamonds can be used to cut glass, but not shatter it. The amount of force needed to apply enough pressure to even pierce a tiny whole in 2 inch thick, heavy duty glass is impossible for a human to supply. We can assume that the glass surrounding the Crown Jewels is every type of "proof" possible, i.e. bullet proof, fire proof, and shatter proof. The laminated style of safety glass has an inter-layer that keeps the layers of glass bonded even when broken so it would be nearly impossible to shatter and separate the glass enough to climb though. I'm thinking that Moriarty must have used some other method to make the glass appear as if it was shattered and the trick with the diamond was all for theatrics.

The Boomerang That Killed a Man

There happened to be a very interesting case a few days ago involving the accidental killing of a young man by his own boomerang.  I found the boomerang itself to be quite remarkable and examined the science of it's inner workings.  The boomerang works on a combination of different physical principles, such as lift and how it generates torque, which allows the boomerang to curve back around to its thrower.  A boomerang spins as it flies, which makes it different than an airplane's wings because the aerodynamic lift is not the same across all parts of the boomerang simultaneously.  This unfortunate young man had not been paying very good attention to his boomerang and as he turned his head, his own recreational tool came back and hit him in the side of the head, causing blunt trauma to his head, bruising the inside and causing pressure from the blood to kill him.

The Bomb Vest Threat

Yesterday I was threatened with a bomb by Moriarty, a criminal mastermind who dislikes Sherlock and I.  At one point, we reached a standoff with Moriarty, in which a bomb vest lay between Sherlock and I and Moriarty, and snipers had trained their guns on Sherlock and I at Moriarty's request.  Sherlock had a gun pointed at the bomb vest, ready to blow it up.  If he had blown up the vest, which weighed about 2.267 kg, it would have exploded apart into a hundred pieces.  The momentum of the entire thing would be conserved because 0 = m₁v₁ + m₂v₂

Assuming for the purposes of this equation, the bomb would explode into four parts, all equal in size and velocity, then m₁ =0.56675, m₂ = 0.56675, m₃=0.56675, and m₄=0.56675, and they were all traveling in different directions, then the momentum would cancel out and it would equal zero.

Getting a Good Shot

Today was another thrilling day in my new life as Sherlock's sidekick. We were just solving the case of who the serial murderer was (the taxi driver) when Sherlock slipped away. I realized he had been picked up by the psycho taxi driver and so I went looking for him. I got to the building where Sherlock was being held and looked through two separate windows. I saw Sherlock sitting at a table across from the murderer with two pills in his hands (one of which I later found out was full of poison) and a gun to his head. My army instincts kicked in, and I found myself aiming my gun at the taxi driver. I realized however that due to the refraction of light, my aim would be off. I had to allow for the bending of light from the air through the first pane of glass, then through the second pane of glass, and back to the air. When the incident ray goes through the higher density medium (the glass), it bends toward the normal because the wavelengths shorten and the velocity slows. Then when the light leaves the higher density medium (the glass) and enters the lower density medium (the air), the transverse wave will speed up and the wavelength will increase, bending the transmitted ray away from the medium. It then repeats this process again through the second pane of glass. Fortunately, I was able to adjust my shot in time and shot the serial killer before he killed Sherlock.

Catching a Taxi

I met my new flatmate today, his name is Sherlock Holmes.  He's kind of arrogant and long story short, we ended up chasing a taxi that contained who we believed to be a serial murderer.  Even though we knew the taxi was going at about 6.7056 m/s, we were able to catch up to it when we were running at about 2.682 m/s.  I'm not sure how much less distance we traveled in order to have caught up to that taxi, but I know that it took both of us about 95.2 seconds to reach the same point.  Above is a map of the path of the taxi (red) and the path that Sherlock and I took to catch it (green).

If x= tv, and v=6.7056 m/s, and t = 95.2 s, so (6.7056)(95.2) = 638.37312 m for the car
then for Sherlock and I, v=2.682 m/s, and t= 95.2 s, so (2.682)(95.2) = 255.3264 for us
638.37312-255.3264 = 383.04672 m
We traveled about 383 meters less than the taxi to catch up to it!  Amazing!