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PHYC 201 Spring 2024 Cuyamaca College Assignment 1 Name: 1. Consider a water reservoir. The reservoir gradually loses water, because people insist on showering, washing clothes, etc. The ”use rate” R is the rate at which consumers use the water. a. On April 13, between 1 p.m. and 2 p.m., R is 5 gallons per second. How much water was drained from the reservoir between 1 p.m. and 1:30 p.m.? b. At midnight, when everyone is asleep, a big industrial water user suddenly becomes active. Let A denote the amount of water taken from the reservoir (in gallons), with A = 0 at midnight. It turns out that A = 2t2 , with t expressed in seconds. Given this information, calculate R, the use rate, at t = 10 s. (Think of what a rate of change implies from your other classes.) 2. A biologist studies a species of bacteria called FAST. Her research reveals that FAST bacteria reproduce prodigiously. If a bacteria culture contains 10 FAST bacteria at time t = 0, the number of FAST bacteria in the culture at later time t is N (t) = 10+6t+2t2 , where t is expressed in seconds. a. How many FAST bacteria occupy the culture at time t = 10 s? At time t = 11 s? From these answers, calculate how many net bacteria were born during the interval between t = 10 and t = 11 s. Assume no bacteria died. b. Now use calculus to find the birth rate of bacteria (the rate at which new bacteria get born) at time t = 10 s. It may help you to sketch a rough graph of N vs. t. c. Explain, conceptually, why your answers to part (a) and (b) are close but not exactly the same. 1 of 2 PHYC 201 Spring 2024 Cuyamaca College Assignment 1 Name: 3. The following questions come from the class textbook: 1.7: How many years older will you be in 1.00 gigaseconds? (Assume a 365-day year.) 1.14: With a wooden ruler, you measure the length of a rectangular piece of sheet metal to be 12 mm. With micrometer calipers, you measure the width of the rectangle to be 5.98 mm. Use the correct number of significant figures: What is (a) the area of the rectangle; (b) the ratio of the rectangle’s width to its length; (c) the perimeter of the rectangle; (d) the difference between the length and the width; and (e) the ratio of the length to the width? ⃗ has y-component Ay = +9.60m. A ⃗ makes an angle of 32.0o coun1.29: Vector A ⃗ (b) What is the terclockwise from the +y-axis. (a) What is the x-component of A? ⃗ magnitude of A? ⃗ 4.00î + 7.00ĵ and B= ⃗ 5.00î – 2.00ĵ, (a) find the magnitude 1.38: Given two vectors A= ⃗of each vector; (b) use unit vectors to write an expression for the vector difference A ⃗ and (c) find the magnitude and direction of the vector difference A ⃗ – B. ⃗ (d) In a B; ⃗ B, ⃗ and A ⃗ – B, ⃗ and show that your diagram agrees qualitatively vector diagram show A, with your answer to part (c). ⃗ and B ⃗ given in Exercise 1.38. (b) 1.42: (a) Find the scalar product of the vectors A Find the angle between these two vectors. ⃗ xB ⃗ (expressed in unit vectors) of the two vectors 1.44: Find the vector product A given in Exercise 1.38. What is the magnitude of the vector product? 2 of 2
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