## Module 4 Class Activities

You are watching people practicing archery when you wonder how fast an arrow is shot from a bow. With a flash of insight you remember your physics and see how you can easily determine what you want to know by a simple measurement. You ask one of the archers to pull back her bow string as far as possible and shoot an arrow horizontally. The arrow strikes the ground at an angle of 86° from the vertical at 100 feet from the archer.

At your job with an insurance company, you have been asked to help with the investigation of a tragic “accident.” At the scene is a road that runs straight down a hill with a slope of 10 degrees below the horizontal. At the bottom of the hill, the road goes horizontally for a very short distance, then ends in a parking lot overlooking a cliff. The cliff has a vertical drop of 400 feet to the horizontal ground below where the wrecked car lies 30 feet from the base of the cliff. The only witness claims that the car was parked somewhere on the hill, he can’t exactly remember where, and the car just began coasting down the road. The witness did not hear an engine and thinks that the driver was drunk and passed out knocking off his emergency brake. The witness also remembers that the car took about 3 seconds to get down the hill. The lead investigator drops a stone from the edge of the cliff and, from the sound of it hitting the ground below, determines that it takes 5.0 seconds to fall to the bottom. Based on that information, you are told to calculate the car’s average acceleration coming down the hill using the statement of the witness and the other facts in the case. You are reminded to write down all of your assumptions so the investigation team can evaluate the applicability of your calculation to this situation.

The earth has a radius of 6380 km and turns around once on its axis in 24 h.

(a) What is the centripetal acceleration of an object at the earth’s equator? Give your answer in m/s^{2} and as a fraction of *g*.

(b) If *a*_{c} at the equator is greater than *g*, objects will fly off the earth’s surface and into space. (We will see the reason for this in module 6.) What would the period of the earth’s rotation have to be for this to occur?