A Damnable Man: Who Killed Adam Able?

[merx7ii]

Homework Statement

A warm, quiet, humid night in the city -- the traffic has died away and there isn't even a cooling breeze. There is a busy hotel that is so well built that sounds don't carry through the windows. The hotel has impressively large rooms. This is obvious from the outside because there is more space between floors and rooms than normal. The rooms appear to have 14 foot high ceilings, nice plate glass windows that slide open, and fully two foot-thick floors for ducting and sound insulation. This is the type of hotel that people like to stay at when someone else is paying the bill.

Outside the hotel, a man is speaking quietly with the doorman. He begins to measure the plush runway carpet for replacement. He is reeling out the tape between the hotel and the curb when a scream breaks the quiet. Looking up, he sees a man falling toward him. Stunned, he drops the tape measure and runs for the safety of the hotel. The doorman stands, horrified, as the man completes his fall with a sickening sound, ensuring that the carpet must be replaced. At intense times, people can think of the strangest things, and the carpet-man finds this to be true . . .all he can think of are the bloodstains left on his tape measure. Even if they are cleaned off, he doesn't think he can use it again without thinking of tonight. Even measuring with another will be hard, and 18 feet will be indelibly marked in his memory -- that's where the blood stains are.

The police arrive and quickly conclude that it is not a suicide – among the victim's personal effects, they find pictures and records that indicate he has been blackmailing four other occupants of the hotel. He also has bruises on his shins where the ledge at the bottom of the tall hotel window would have hit them; he must have been pushed pretty hard. Adam Able is the dead man's name, as it appears on the driver's license in his wallet. His license indicates that Adam was 5'11" tall and weighed 160 lb. He has been blackmailing Adrianna Myers, a frail widow in Room 356; Steven Caine, a newspaper reporter in Room 852; Mark Johnson, a body builder in Room 1956; and Stanley Michaels, an actor in Room 2754. All of the suspects admit they were in their rooms at the time of the murder.

WHO KILLED ADAM ABLE?

Homework Equations

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The Attempt at a Solution

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[Beaker87]

This appears to be a projectile motion problem. You need to find out whose room Adam was pushed out of.

First of all, the room numbers could indicate what floor they are on, i.e. room 656 would be on the 6th floor, and room 2108 would be the 21st floor. The story tells you how high each room is (14 ft) and the thickness of the floors (2ft.) Using this, you can figure out how high up each room is.

Now you need to figure out how fast Adam was shoved. You will need to make an assumption to do this, however a decent approach to this, is to have a friend on a skateboard, or a wheeled device of any kind. Shove him, and measure how fast he goes. Be careful not to hurt your friend, as you are friends. Then assume that the old lady shoved a bit (maybe -40%) less hard than you, and the body builder shoved a bit harder (maybe 30%) harder than you.

Now figure out how far from the hotel Adam would land if he were shoved from the height of each room. You want to know which room would make him land 18 ft (as that's what the tape measure said) from the hotel.

 

[merx7ii]

Luckily I got to solve it already! Thanks anyway :) Got it this way: I assumed the horizontal velocity to be 2m/s so that's about 7ft/s. Using the sol'n Vx=x/t, I got t=x/Vx, so that's about 3 seconds. I substituted everything to the equation y=Voyt+(-g)t^2 and got 144m, exactly. That means he fell from above the 9th floor (since 144m/16m(per floor)), and the person there is Mark Johnson the body builder.

There! In case anybody else needs it :)

 

[merx7ii]

This appears to be a projectile motion problem. You need to find out whose room Adam was pushed out of.

First of all, the room numbers could indicate what floor they are on, i.e. room 656 would be on the 6th floor, and room 2108 would be the 21st floor. The story tells you how high each room is (14 ft) and the thickness of the floors (2ft.) Using this, you can figure out how high up each room is.

Now you need to figure out how fast Adam was shoved. You will need to make an assumption to do this, however a decent approach to this, is to have a friend on a skateboard, or a wheeled device of any kind. Shove him, and measure how fast he goes. Be careful not to hurt your friend, as you are friends. Then assume that the old lady shoved a bit (maybe -40%) less hard than you, and the body builder shoved a bit harder (maybe 30%) harder than you.

Now figure out how far from the hotel Adam would land if he were shoved from the height of each room. You want to know which room would make him land 18 ft (as that's what the tape measure said) from the hotel.

Does it mean that room 1956 would be on the 19th floor? Not the 10th?

 

[Beaker87]

Does it mean that room 1956 would be on the 19th floor? Not the 10th?

Based on MY assumptions about floor height, room 1956 means room 56 on the 19th floor. Many buildings use the numbering scheme I just described, however some buildings do not.

 

[justAsking]

how could you say that johnson was the one and not michaels?