=Portfolio Problem 1. A particle of mass m is dropped (i.e., falls down withzero initial velocity) at time t 0 from height h. If the particle is subject togravitational acceleration only, i.e., a = −gk, determine its speed as it hits theground by solving explicitly the expressions for its velocity and position. Next,verify your result using dimensional analysis, assuming that the general relationis of the form v = khag³m, where k is a dimensionless constant.

Answered: Image /qna-images/answer/9ea701a0-9d81-4073-a945-d85c2baedb64.jpg

Answered: = Portfolio Problem 1. A particle of…

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter3: Motion In Two Dimensions

Section: Chapter Questions

Problem 42P: A landscape architect is planning an artificial waterfall in a city park. Water flowing at 1.70 m/s...

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A student at the top of a building of height h throws one ball upward with a speed of vi and then throws a second ball downward with the same initial speed vi. Just before it reaches the ground, is the final speed of the ball thrown upward (a) larger, (b) smaller, or (c) the same in magnitude, compared with the final speed of the ball thrown downward?
(a) A car speedometer has a 5% uncertainty. What is the range of possible speeds when it reads 90 km/h? (b) Convert this range to miles per how. Note 1 km = 0.6214 mi.
Acceleration a has the dimensions of length per time squared, speed v has the dimensions of length per time, and radius r has the dimension of length. Which of the following expressions may be correct? Explain your answer in each case. a. a = vr b. a = v/r c. a = v2/r d. a = v/r2
Figure P2.33 shows the y-position (in blue) of a particle versus time. a. What is the average velocity of the particle during the time interval t = 1.00 s to t = 3.50 s? b. Using the tangent to the curve (shown as the orange line in the figure), what is the instantaneous velocity of the particle at t = 1.50 s? c. At what time is the velocity of the particle equal to zero? FIGURE P2.33
Unreasonable results At the end of a race, a runner decelerates from a velocity of 9.00 m/s at a rate of 2.00m/s2 . (a) How far does she travel in the next 5.00 s? (b) What is her final velocity? (c) Evaluate the result. Does it make sense?
After a ball rolls off the edge of a horizontal table at time t = 0, its velocity as a function of time is given by v=1.2i9.8tj where v is in meters per second and t is in seconds. The balls displacement away from the edge of the table, during the time interval of 0.380 s for which the ball is in flight, is given by r=00.3803vdt To perform the integral, you can use the calculus theorem [A+Bf(x)]dx=Adx+Bf(x)dx You can think of the units and unit vectors as constants, represented by A and B. Perform the integration to calculate the displacement of the ball from the edge of the table at 0.380 s.
A pirate has buried his treasure on an island with five trees located at the points (30.0 m, 20.0 m), (60.0 m, 80.0 m), (10.0 m, 10.0 m), (40.0 m, 30.0 m), and (70.0 m, 60.0 m), all measured relative to some origin, as shown in Figure P1.69. His ships log instructs you to start at tree A and move toward tree B, but to cover only one-half the distance between A and B. Then move toward tree C, covering one-third the distance between your current location and C. Next move toward tree D, covering one-fourth the distance between where you are and D. Finally move toward tree E, covering one-fifth the distance between you and E, stop, and dig. (a) Assume you have correctly determined the order in which the pirate labeled the trees as A, B, C, D, and E as shown in the figure. What are the coordinates of the point where his treasure is buried? (b) What If? What if you do not really know the way the pirate labeled the trees? What would happen to the answer if you rearranged the order of the trees, for instance, to B (30 m, 20 m), A (60 m, 80 m), E (10 m, 10 m), C (40 m, 30 m), and D (70 m, 60 m)? State reasoning to show that the answer does not depend on the order in which the trees are labeled. Figure 1.69
A driver uniformly accelerates his car such that a=6.851im/s2. a. Assuming he starts from rest, find the velocity of the car after it has accelerated for 4.55 s. b. If immediately after that 4.55 s the driver lays off the accelerator, slams on the brakes, and comes to a stop in the subsequent 5.62 s, what is the acceleration he experiences during that time, assuming the acceleration is constant?
A car is traveling at a speed of 33 m/s. (a) What is its speed in kilometers per hour? (b) Is it exceeding the 90 km/h speed limit?
A garden snail named Archie, owned by Carl Branhorn of Pott Row, England, covered a 33-cm course in 2.0 min at the 1995 World Snail Racing Championships, held in Longhan, England (Fig. P1.13). Determine Archies average speed Sav = d/t in the appropriate SI units.
Two bicyclists in a sprint race begin from rest and accelerate away from the origin of an xy coordinate system. Miguels acceleration is given by (0.700i + 1.00j) m/s2, and Lances acceleration is given by (1.20i + 0.300j) m/s2. a. What is Miguels acceleration with respect to Lance? b. What is Miguels speed with respect to Lance after 4.50 s have elapsed? c. What is the distance separating Miguel and Lance after 4.50 s have elapsed?
Two sprinters start a race along a straight track at the same time and cross the finish line at the same time. a. Are their average velocities necessarily equal? Explain. b. Are their instantaneous velocities necessarily always equal? Explain. c. Are their final velocities necessarily equal? Explain.

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