If an object with mass m is dropped from rest, one model for its speed v after
Question:
If an object with mass m is dropped from rest, one model for its speed v after t seconds, taking air resistance into account, is
where t is the acceleration due to gravity and c is a positive constant. (In Chapter 9 we will be able to deduce this equation from the assumption that the air resistance is proportional to the speed of the object; c is the proportionality constant.)
(a) Calculate limt t→ ∞ v. What is the meaning of this limit?
(b) For fixed t, use 1’Hospital’s Rule to calculate lim c → 0 + v. What can you conclude about the velocity of a falling object in a vacuum?
-et/m - (1 – e ¯ct/m mg
Step by Step Answer:
a mgc which is the speed the objec...View the full answer
Related Video
In Physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity, i.e., to accelerate. Force can also be described intuitively as a push or a pull. A force has both magnitude and direction, making it a vector quantity. In this video, the concept of force and torque is demonstrated with the practical application of changing the flat tire of the car.
Students also viewed these Mathematics questions
-
An object with mass m is dropped from rest and we assume that the air resistance is proportional to the speed of the object. If s (t) is the distance dropped after seconds, then the speed is v = s...
-
In Chapter 9 we will be able to show, under certain assumptions, that the velocity v(t) of a falling raindrop at time t is where t is the acceleration due to gravity and is the terminal velocity of...
-
In Chapter 9 we will be able to show, under certain assumptions, that the velocity v(t) of a falling raindrop at time t is V(t) = v* (1 - e-gt/v*) where t is the acceleration due to gravity and v* is...
-
1. The following are selected accounts taken from the adjusted trial balances of the Purell Merchandise company on December 31, 2021: Inventory, January 1, 2021 Selling expenses Loss on sale of...
-
Describe the role of professional judgment in ethical leadership as it pertains to accountants and auditors.
-
It was reported within the chapter that some years ago the chairperson of Australias biggest wine producer, Southcorp Ltd, was critical of the requirements incorporated within AASB 141 because it...
-
Rank these three living things from largest to smallest: (a) a tuberculosis bacterium, a prokaryote; (b) bakers yeast, a single-celled eukaryote; (c) a human, a multicellular eukaryote.
-
Carl, Barrowman, and Cribbins are partners who share profits and losses 50%, 30%, and 20%, respectively. Their capital balances are $100,000, $60,000, and $40,000, respectively. Instructions (a)...
-
On 1 March 20X0 an entity that has a functional currency of CU buys a retail outlet in another country (local currency = FCU) for FCU500,000 to sell products to customers in the other country. The...
-
Brown transfers Blackacre to XYZ Corp., a newly formed corporation, in exchange for 140 shares of its common stock having a FMV of $70,000. Blackacre had a basis in Brown's hands of $10,000. At the...
-
Investigate the family of curves f (x) = e x - cx. In particular, find the limits as x and determine the values of c for which f has an absolute minimum. What happens to the minimum points as c...
-
Light enters the eye through the pupil and strikes the retina, where photo receptor cells sense light and color. W. Stanley Stiles and B. H. Crawford studied the phenomenon in which measured...
-
Interpersonal violence (e.g., rape) generally leads to psychological stress for the victim. Clinical Psychology Review (Vol. 15, 1995) reported on the results of all recently published studies of the...
-
2. Firms HD and LD are identical except for their use of debt and the interest rates they pay--HD has more debt and thus must pay a higher interest rate. Based on the data given below, how much...
-
One year ago today you bought a 6% coupon bond with a face value of 100 and 5 years to maturity for a price of 102.47. The bond pays interest annually. In the meantime the yield to maturity for the...
-
Beyonce went to the mall and saw a massage chair that she would have to take a loan out for $6,500 to purchase. The bank said that she could get a simple interest rate of 8% for 5 years. What is the...
-
When a 500-g statue of a falcon suspended from a spring is immersed in water, the scale reads 400 g, and when immersed in benzene, the scale reads 412 g. Determine the density of benzene.
-
In what distance can a 6 0 0 0 lb truck be stopped from a speed of 4 4 ft / s , if the coefficient of friction between tires and roadway is 7 0 %.
-
Explain in words the difference between Laspeyres and Paasche indexes.
-
Identify the tax issues or problems suggested by the following situations. State each issue as a question. Jennifer did not file a tax return for 2007 because she honestly believed that no tax was...
-
Find the length of the curve correct to four decimal places. (Use a calculator to approximate the integral.) r(t) = (t 2 , t 3 , t 4 ), 0 < t < 2
-
Find the length of the curve correct to four decimal places. (Use a calculator to approximate the integral.) r(t) = (t, e -t , te -t l, + < t < 3
-
Find the length of the curve correct to four decimal places. (Use a calculator to approximate the integral.) r(t) = (cos t, 2t, sin 2t), from (1, 0, 0) to (1, 4, 0)
-
You will want to start by looking over the list of requirements for the videos and take some notes on how you will explain and demonstrate each one. Demonstrate dispute resolution techniques....
-
Two parallel infinite conductive plates are placed at a distance d = 3.0 mm. These two plates carry surface charge densities +4 and -2, respectively, where = 1.1 nC/m2. What is the modulus of the...
-
Compare and contrast the various references that these artists make to the world beyond the scenes they depict? (city life, continuity with an actual chapel). Why do you think that Campin included...
Study smarter with the SolutionInn App