FORENSICS · ALLEY CONTRACT CHECK

The second-floor window was found open. A ladder lay in the alley below it, and two scuffs in the grime sit below the window. The department's ladder rule: to climb through a window, the ladder rests on the sill and at least 0.95 m of it has to stand past the sill. Was this ladder long enough?

Scuff marks on level ground are 2.0 meters from a vertical wall. A ladder footed at the marks rests on a windowsill 3.6 meters above the ground. To climb through the window, at least 0.9 meters of the ladder must extend past the sill. What is the minimum length of the ladder, to the nearest tenth of a meter?

Answer 5.1 m (geometry 5.0683, accepted ±0.05)

From the scuffs, a climber needs at least 5.1 m of ladder. The ladder in the alley is 5.4 m and stands 1.28 m past the sill: enough to climb in.

Measurements and givens

Misses

The second-floor window was found open. A ladder lay in the alley below it, and two scuffs in the grime sit below the window. The department's ladder rule: to climb through a window, the ladder rests on the sill and at least 0.95 m of it has to stand past the sill. Was this ladder long enough?

Scuff marks on level ground are 2.0 meters from a vertical wall. A ladder footed at the marks rests on a windowsill 3.6 meters above the ground. To climb through the window, at least 0.9 meters of the ladder must extend past the sill. What is the minimum length of the ladder, to the nearest tenth of a meter?

Answer 5.1 m (geometry 5.0683, accepted ±0.05)

From the scuffs, a climber needs at least 5.1 m of ladder. The ladder in the alley is only 4.8 m and stands 0.68 m past the sill: too little to climb in.

Measurements and givens

Misses

The service door's alarm logged it opening at 23:42:06.0. At 23:42:08.5 a patrol car's lights swept the alley mouth, and its dash camera shows the alley empty. The theory: someone came out the door, ran around the stacked cases and was gone before the lights hit. Running empty-handed, a person manages about 6.0 m/s over a distance this short.

From a doorway, a person runs a route in two straight legs. The first leg ends at a point 2.4 meters farther along the wall and 1.8 meters out from it. The second leg runs 5.6 meters parallel to the wall. The person covers the whole route in 2.5 seconds at a constant speed. What is that speed, in meters per second, to the nearest tenth?

Answer 3.4 m/s (geometry 3.4400, accepted ±0.05)

The route takes 3.4 m/s. Running empty-handed, a person manages about 6.0. Someone could have been gone before the lights hit.

Measurements and givens

Misses

The service door's alarm logged it opening at 23:42:06.0. At 23:42:08.5 a patrol car's lights swept the alley mouth, and its dash camera shows the alley empty. The theory: someone came out the door, ran around the stacked cases and was gone before the lights hit. Whoever it was carried the missing equipment case, 32 kg, and a person carrying that much manages about 3.0 m/s.

From a doorway, a person runs a route in two straight legs. The first leg ends at a point 2.4 meters farther along the wall and 1.8 meters out from it. The second leg runs 5.6 meters parallel to the wall. The person covers the whole route in 2.5 seconds at a constant speed. What is that speed, in meters per second, to the nearest tenth?

Answer 3.4 m/s (geometry 3.4400, accepted ±0.05)

The route takes 3.4 m/s, faster than the 3.0 m/s a person manages carrying the case. Whoever opened the door was still in the alley when the lights hit.