Question

There’s a huge icicle hanging from the roof of your two-story house. It overhangs a lower eave off of the first floor. Your housemate’s car is parked about 5 feet directly out from the edge of the lower eave. The friend looks out the top floor window and says, “Uh oh, if that icicle falls, it looks like it could hit my car.” You say, “Nah, I wouldn’t worry.” Then you part ways. But you get to thinking... “Maybe I spoke too soon.” Instead of doing the easy thing, and suggesting that your housemate move their car just in case, you decide to make a little estimate to check whether or not you should worry. You figure the distance between the icicle and lower eave is about 8 feet. The lower eave—made of metal—is slanted at about 30 degrees, and the icicle would slide on it for about a foot before leaving the edge if it were to fall. The edge of the eave is about 10 feet off the ground.

Answer 1

Velocity of icicle when it hits the lower eave,

Where H = 8 ft

Component of speed along the eave :

Its acceleration along the eave:

velocity of the icicle when it leaves the eave

Where S = 1ft

If t seconds is the time in which icicle reaches the ground, then using

Solving the quadratic equation

t = 0.62 s

Horizontal distance travelled by icicle in this time

x = 6.8 ft

Considering the length of the car it may hit the car, but if friction in the surface of eave is considerable it may fall behind the car.