Physics 101-2: Introductory Physics I, Fall 2012 Lecture 7

Today: Free-fall. (This is a revised version of Monday’s handout, with two demo problems added).

All objects moving near the earth’s surface, under the influence of gravity and no other forces, have an acceleration

2 ~afree fall = (9.8 m/s , downward).

2 That is, ay = −g and ax = 0. The symbol g = 9.8 m/s denotes the magnitude of ~afree fall

and is positive. (On p. 56, the last equation should read ay = −afree fall = −g, where afree fall denotes the magnitude of ~afree fall.

Question 1: An arrow is launched vertically upward. It moves straight up to a maximum height, then falls to the ground. The trajectory of the arrow is noted (see below). At which point of the trajectory is the arrow’s acceleration the greatest? The least? Ignore air resistance; the only force acting is gravity.

Question 2: An arrow is launched vertically upward. It moves straight up to a maximum height, then falls to the ground. The trajectory of the arrow is noted. Which graph best represents the vertical velocity of the arrow as a function of time? Ignore air resistance; the only force acting is gravity. Physics 101-2, Fall 2012: Lecture 7 p. 2

Question 3: The figure below shows five arrows with differing masses that were launched straight up with the noted speeds. Rank the arrows, from greatest to least, on the basis of the maximum height the arrows reach. Ignore air resistance; the only force acting is gravity.

Demo/Problem 1: Dollar bill reaction time challenge (KJF Problem 2.30). A per- son’s reaction time is generally not quick enough to allow the person to catch a dollar bill dropped between the fingers. If a typical reaction time in this case is 0.25 s, how long would a bill need to be for a person to have a good chance of catching it?

Demo/Problem 2: Superman II Niagara Falls scene. There are many movies that involve free fall, usually in a way that isn’t physically correct. In Superman II, a boy falls over the edge of Niagara Falls, height 51 m. Clark Kent notes his plight, looks for a place to change, changes clothes, and flies to save him. This all takes about 30 s. Neglecting air resistance, how long would Superman would actually have to come to the boy’s aid?

Problem Solving Strategy: Three parts, “Prepare, Solve, Assess.”

1. Prepare: Visual overview—picture, graph, and/or motion diagram. Gather info. (This step is more and more useful for more complicated problems).

2. Solve: Reasoning/math.

3. Assess: Does it make sense? (Fits with experience? Units check out?)