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Umar Sohail Qureshi

Numerade educator

Review. You can think of the work–kinetic energy theorem as a second theory of motion, parallel to Newton's laws in describing how outside influences affect the motion of an object. In this problem, solve parts (a), (b), and (c) separately from parts (d) and (e) so you can compare the predictions of the two theories. A 15.0 -g bullet is accelerated from rest to a speed of 780 $\mathrm{m} / \mathrm{s}$ in a rifle barrel of length $72.0 \mathrm{cm} .$ (a) Find the kinetic energy of the bullet as it leaves the barrel. (b) Use the work-kinetic energy theorem to find the net work that is done on the bullet. (c) Use your result to part (b) to find the magnitude of the average net force that acted on the bullet while it was in the barrel. (d) Now model the bullet as a particle under constant acceleration. Find the constant acceleration of a bullet that starts from rest and gains a speed of 780 $\mathrm{m} / \mathrm{s}$ over a distance of $72.0 \mathrm{cm} .$ (e) Modeling the bullet as a particle under a net force, find the net force that acted on it during its acceleration. (f) What conclusion can you draw from comparing your results of parts (c) and (e)?

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INSTANT ANSWER

For Exercises 19 through 26, construct a probability distribution for the data and draw a graph for the distribution. Statistical Calculators The probability that a college bookstore sells $0,1,2,$ or 3 statistical calculators on any given day is $\frac{4}{9}, \frac{2}{9}, \frac{2}{9},$ and $\frac{1}{9},$ respectively.

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Ma Ednelyn Lim

Numerade educator

Given that 1 mi 1760 yd, determine what conversion factor is appropriate to convert 1849 yd to miles; to convert 2.781 mi to yards.

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Bryan Valdivia

Numerade educator

All of the following are abiotic factors in an ecosystem EXCEPT (A) sunlight (B) wind (C) soil (D) temperature (E) producers

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Supreeta N

Numerade educator

Wingspan and weight The weight $W$ (in pounds) of a bird (that can fly) has been related to the wingspan $L$ (in inches) of the bird by the power function $L=30.6 \mathrm{W}^{0.3952} .$ (In Exercise 1.5 .66 this model will be derived from data.) (a) The bald eagle has a wingspan of about 90 inches. Use the model to estimate the weight of the eagle. (b) An ostrich weighs about 300 pounds. Use the model to order for it to fly. (c) The wingspan of an ostrich is about 72 inches. Use your answer to part (b) to explain why ostriches can't fly.

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AWAITING AN EDUCATOR

How many permutations of the letters ABCDEFGH contain a) the string ED? b) the string CDE? c) the strings BA and FGH? d) the strings AB, DE, and GH? e) the strings CAB and BED? f ) the strings BCA and ABF?

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Hubert Agamasu

Numerade educator

Push-ups. To strengthen his arm and chest muscles, an 82 kg athlete 2.0 m tall is doing a series of push-ups as shown in Figure $10.58 .$ His center of mass is 1.15 m from the bottom of his feet, and the centers of his palms are 30.0 $\mathrm{cm}$ from the top of his head. Find the force that the floor exerts on each of his feet and on each hand, assuming that both feet exert the same force and both palms do likewise. Begin with a free-body diagram of the athlete.

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Teresa Fuston

Numerade educator

Jean bought a $\$ 1,980$ snow thrower on the installment plan. The installment agreement included a 10$\%$ down payment and 18 monthly payments of $\$ 116$ each. a. How much is the down payment? b. What is the total amount of the monthly payments? c. How much did Jean pay for the snow thrower on the installment plan? d. What is the fi nance charge?

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INSTANT ANSWER

ART A sculpture has a hyperbolic cross section (see figure). (a) Write an equation that models the curved sides of the sculpture. (b) Each unit in the coordinate plane represents 1 foot. Find the width of the sculpture at a height of 5 feet.

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INSTANT ANSWER

What is the negation of each of these propositions? a) Steve has more than 100 $\mathrm{GB}$ free disk space on his laptop. b) Zach blocks e-mails and texts from Jennifer. c) $7 \cdot 11 \cdot 13=999$ . d) Diane rode her bicycle 100 miles on Sunday.

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Daniel M.