2. (Final Velocity of a Falling Object) Read the problem description for Problem 4.3 on page 107 of the text. Assume that, as described there, the final velocity (terminal velocity) depends on the acceleration due to gravity, the mass affected by the air resistance, and the density of the air. Instead of the given directions, do the following the animal, the area of the cross section that is (a.) For each of the four quantities (acceleration due to gravity, mass, area of cross section, density of air), look at what the problem descrip- tion says about how the final velocity varies with the quantity. For each of the four quantities, briefly explain why what the problem description says makes sense (b.) Find a dimensionally feasible expression for the final velocity, by finding a dimensionless group involving all the quantities including the final velocity and then solving for the final velocity. For this homework problem, you do not need to be certain that your formula is correct. However, you do need to show your reader that your formula for the final velocity has the correct units. 4.3. In the fall from the roof of a tall building, an ant will probably not get hurt, a mouse may suffer a shock but could walk or limp away uninjured, a cat may lose more than one of its seven lives, a human dies almost certainly, while an elephant would certainly make a huge mess. The final velocity Ufinal is the main factor deciding the fate of the animal: The forces due to the deceleration from vfinal to a complete stop are the source of the damage (a) Analyze the question using dimensional analysis. Here is a suggestion: Write Vinal f(g, m, A, p) where g 9.8 m/s2 is the acceleration due to gravity, m is the mass of the animal, A is the area of the cross section that is affected by the air resistance, andp is the density of the air. Notice that once you find the II-numbers, you should try to come up with an expression that makes physical sense (e.g., the velocity should be larger for larger animals, smaller for higher air density, smaller for weaker gravity, and smaller for larger cross sections) (b) For comparison, solve the problem using Newton's Second Law of Mo- tion, Ftot Fgr +Fair =ma, a(t)v'(t) z"(t) is the downward acceleration, Fgr is the where a = gravitational force, Fgr mg, and Fair is the air resistance, assumed to be of the form =v(t), air= where a is some constant

2. (Final Velocity of a Falling Object) Read the problem description for Problem 4.3 on page 107 of the text. Assume that, as described there, the final velocity (terminal velocity) depends on the acceleration due to gravity, the mass affected by the air resistance, and the density of the air. Instead of the given directions, do the following the animal, the area of the cross section that is (a.) For each of the four quantities (acceleration due to gravity, mass, area of cross section, density of air), look at what the problem descrip- tion says about how the final velocity varies with the quantity. For each of the four quantities, briefly explain why what the problem description says makes sense (b.) Find a dimensionally feasible expression for the final velocity, by finding a dimensionless group involving all the quantities including the final velocity and then solving for the final velocity. For this homework problem, you do not need to be certain that your formula is correct. However, you do need to show your reader that your formula for the final velocity has the correct units. 4.3. In the fall from the roof of a tall building, an ant will probably not get hurt, a mouse may suffer a shock but could walk or limp away uninjured, a cat may lose more than one of its seven lives, a human dies almost certainly, while an elephant would certainly make a huge mess. The final velocity Ufinal is the main factor deciding the fate of the animal: The forces due to the deceleration from vfinal to a complete stop are the source of the damage (a) Analyze the question using dimensional analysis. Here is a suggestion: Write Vinal f(g, m, A, p) where g 9.8 m/s2 is the acceleration due to gravity, m is the mass of the animal, A is the area of the cross section that is affected by the air resistance, andp is the density of the air. Notice that once you find the II-numbers, you should try to come up with an expression that makes physical sense (e.g., the velocity should be larger for larger animals, smaller for higher air density, smaller for weaker gravity, and smaller for larger cross sections) (b) For comparison, solve the problem using Newton's Second Law of Mo- tion, Ftot Fgr +Fair =ma, a(t)v'(t) z"(t) is the downward acceleration, Fgr is the where a = gravitational force, Fgr mg, and Fair is the air resistance, assumed to be of the form =v(t), air= where a is some constant