A stone is thrown from the top of a building upward at an angle of 26.0...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
A stone is thrown from the top of a building upward at an angle of 26.0° to the horizontal with an initial speed of 21.0 m/s as shown in the figure. The height from which the stone is thrown is 45.0 m above the ground. (0, 0) 45.0 m *= ? y=-45.0 m A stone is thrown from the top of a building. (a) How long does it take the stone to reach the ground? SOLUTION Conceptualize Study the figure, in which we have indicated the trajectory and various parameters of the motion of the stone. According to the figure, from what set of coordinates is the stone thrown? O (-45.0 m, 0) O (0, 0) O (0, 45.0 m) Categorize We categorize this problem as a projectile motion problem. The stone is modeled as a particle under constant acceleration in the y-direction and a particle under constant velocity in the x-direction. Analyze We have the information x, = y, = 0, y; = -45.0 m, a, = -g, and v, = 21.0 m/s (the numerical value of y, is negative because we have chosen the top of the building as the origin). Find the initial x- and y-components of the stone's velocity (in m/s): Vxi = v, cos(e) = 18.9 Vyi = v, sin(8,) = 9.21 V m/s m/s Express the vertical position of the stone from the particle under constant acceleration model (Use the following as necessary: Va g, and t. Do not substitute numerical values; use variables only.): Yf = Y; + vyit + Find the initial x- and y-components of the stone's velocity (in m/s): Vxi = v, cos(8) = 18.9 Vyi = v, sin(8,) = 9.21 V m/s V m/s Express the vertical position of the stone from the particle under constant acceleration model (Use the following as necessary: v 9, and t. Do not substitute numerical values; use variables only.): Y; = Y, + vyit + ayr? Substitute numerical values: m/s)t + 글(-9.80 m/s)2 -45.0 m = 0 + 9.21 Solve the quadratic equation to calculate t (in s): t = 3.03 ४ s (b) What is the speed of the stone just before it strikes the ground? SOLUTION Use the velocity equation in the particle under constant acceleration model to obtain the y-component of the velocity of the stone just before it strikes the ground (Use the following as necessary: v 9, and t. Do not substitute numerical values; use variables only.): 1 "y = Vy -ayr? Substitute numerical values (Enter your answer in m/s.): Vyf = m/s Use this component with the horizontal component v = v = 18.9 m/s to find the speed of the stone (in m/s) at t: VE = V V + Vyf m/s Finalize Is it reasonable that the y-component of the final velocity is negative? Is it reasonable that the final speed is larger than the initial speed of 21.0 m/s? EXERCISE The following questions present a twist on the scenario above to test your understanding. Suppose another stone is thrown horizontally from the same building. If it strikes the ground 56 m away, find the following values. (Assume angles above the horizontal are positive.) Hint (a) time of flight (in s) Finalize Is it reasonable that the y-component of the final velocity is negative? Is it reasonable that the final speed is larger than the initial speed of 21.0 m/s? EXERCISE The following questions present a twist on the scenario above to test your understanding. Suppose another stone is thrown horizontally from the same building. If it strikes the ground 56 m away, find the following values. (Assume angles above the horizontal are positive.) Hint (a) time of flight (in s) (b) initial speed (in m/s) m/s (c) speed (in m/s) and angle (in degrees) with respect to the horizontal of the velocity vector at impact speed m/s angle If the stone were thrown harder, and left with 1.5 times the initial speed, you might expect it to go farther, but how exactly does that happen? (d) Throwing the stone horizontally at 1.5 times the previous speed multiplies the time to reach the ground by what factor? (e) The horizontal component of the velocity is multiplied by what factor? (f) How many times farther does the stone land from the building? Need Help? Read It .5/4 Points] DETAILS PREVIOUS ANSWERS SERPSE10 4.AE.001. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Motion in a Plane A particle moves in the xy-plane, starting from the origin at t = 0 with an initial velocity having an x-component of 20 m/s and a y-component of -10 m/s. The particle experiences an acceleration in the x-direction, given by a, = 4.5 m/s2. A stone is thrown from the top of a building upward at an angle of 26.0° to the horizontal with an initial speed of 21.0 m/s as shown in the figure. The height from which the stone is thrown is 45.0 m above the ground. (0, 0) 45.0 m *= ? y=-45.0 m A stone is thrown from the top of a building. (a) How long does it take the stone to reach the ground? SOLUTION Conceptualize Study the figure, in which we have indicated the trajectory and various parameters of the motion of the stone. According to the figure, from what set of coordinates is the stone thrown? O (-45.0 m, 0) O (0, 0) O (0, 45.0 m) Categorize We categorize this problem as a projectile motion problem. The stone is modeled as a particle under constant acceleration in the y-direction and a particle under constant velocity in the x-direction. Analyze We have the information x, = y, = 0, y; = -45.0 m, a, = -g, and v, = 21.0 m/s (the numerical value of y, is negative because we have chosen the top of the building as the origin). Find the initial x- and y-components of the stone's velocity (in m/s): Vxi = v, cos(e) = 18.9 Vyi = v, sin(8,) = 9.21 V m/s m/s Express the vertical position of the stone from the particle under constant acceleration model (Use the following as necessary: Va g, and t. Do not substitute numerical values; use variables only.): Yf = Y; + vyit + Find the initial x- and y-components of the stone's velocity (in m/s): Vxi = v, cos(8) = 18.9 Vyi = v, sin(8,) = 9.21 V m/s V m/s Express the vertical position of the stone from the particle under constant acceleration model (Use the following as necessary: v 9, and t. Do not substitute numerical values; use variables only.): Y; = Y, + vyit + ayr? Substitute numerical values: m/s)t + 글(-9.80 m/s)2 -45.0 m = 0 + 9.21 Solve the quadratic equation to calculate t (in s): t = 3.03 ४ s (b) What is the speed of the stone just before it strikes the ground? SOLUTION Use the velocity equation in the particle under constant acceleration model to obtain the y-component of the velocity of the stone just before it strikes the ground (Use the following as necessary: v 9, and t. Do not substitute numerical values; use variables only.): 1 "y = Vy -ayr? Substitute numerical values (Enter your answer in m/s.): Vyf = m/s Use this component with the horizontal component v = v = 18.9 m/s to find the speed of the stone (in m/s) at t: VE = V V + Vyf m/s Finalize Is it reasonable that the y-component of the final velocity is negative? Is it reasonable that the final speed is larger than the initial speed of 21.0 m/s? EXERCISE The following questions present a twist on the scenario above to test your understanding. Suppose another stone is thrown horizontally from the same building. If it strikes the ground 56 m away, find the following values. (Assume angles above the horizontal are positive.) Hint (a) time of flight (in s) Finalize Is it reasonable that the y-component of the final velocity is negative? Is it reasonable that the final speed is larger than the initial speed of 21.0 m/s? EXERCISE The following questions present a twist on the scenario above to test your understanding. Suppose another stone is thrown horizontally from the same building. If it strikes the ground 56 m away, find the following values. (Assume angles above the horizontal are positive.) Hint (a) time of flight (in s) (b) initial speed (in m/s) m/s (c) speed (in m/s) and angle (in degrees) with respect to the horizontal of the velocity vector at impact speed m/s angle If the stone were thrown harder, and left with 1.5 times the initial speed, you might expect it to go farther, but how exactly does that happen? (d) Throwing the stone horizontally at 1.5 times the previous speed multiplies the time to reach the ground by what factor? (e) The horizontal component of the velocity is multiplied by what factor? (f) How many times farther does the stone land from the building? Need Help? Read It .5/4 Points] DETAILS PREVIOUS ANSWERS SERPSE10 4.AE.001. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Motion in a Plane A particle moves in the xy-plane, starting from the origin at t = 0 with an initial velocity having an x-component of 20 m/s and a y-component of -10 m/s. The particle experiences an acceleration in the x-direction, given by a, = 4.5 m/s2.
Expert Answer:
Related Book For
Calculus Early Transcendentals
ISBN: 978-0321947345
2nd edition
Authors: William L. Briggs, Lyle Cochran, Bernard Gillett
Posted Date:
Students also viewed these physics questions
-
A stone is thrown from the top of a building upward at an angle µ to the horizontal and with an initial speed of v0 as shown in the figure. If the height of the building is H, derive a formula...
-
A ball is thrown from the top of a 100-foot tower with a velocity of 28 feet per second. (a) Find the equation that represents the parabolic path. (b) How far does the ball travel horizontally before...
-
A stone thrown from the top of a building is given an initial velocity of 20.0 m/s straight upward. The stone is launched 50.0 m above the ground, and the stone just misses the edge of the roof on...
-
In Exercises 1138, use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Slope = 2, passing through (3, 5)
-
Software Plus Corporation produces flight and driving simulations and games for personal computers. The president has a complaint about the accounting for support department costs. He points to the...
-
Question 4 Not complete Marked out of 30.00 Flag question Cost of Production Report: No Beginning Inventories Oregon Paper Company produces newsprint paper through a special recycling process using...
-
If the relevant price indices for trade accounts receivable and trade accounts payable are as follows, calculate the monetary working capital adjustment for Seafield Ltd, using the details given in...
-
RLF Company sells office equipment and supplies to many organizations in the city and surrounding area on contract terms of 2/10, n/30. In the past, over 75% of the credit customers have taken...
-
Required information Use the following information for the Exercises below. (Algo) [The following information applies to the questions displayed below.] Megamart provides the following information on...
-
Lombard Ltd has been offered a contract for which there is available production capacity. The contract is for 20,000 identical items, manufactured by an intricate assembly operation, to be produced...
-
Basket Corp. produces and sells a single product. Standards have been established for the product as follows: Direct Materials per unit Direct Labor per unit 8 pounds @ $ 4.00 per pound 3 hours @ $...
-
Schoch-Spana points out that communication from authorities during disasters such as pandemics needs to be frequent, consistent, and honest. To what degree did authorities achieve this goal during...
-
Anthropology includes archaeology, biological anthropology, cultural anthropology, and linguistics. What are the similarities and differences among these approaches, and in what ways do they share...
-
The organizational structure chart in the text is a simplified version. Go to www.conference-board.org, follow the Organization Charts link, and then the Click here to see a sample chart link. What...
-
Understanding the meaning of a communication is often much more than simply understanding the words that have been said. The connection between language and the body runs deep. When we talk, we often...
-
How are internal auditing and independent auditing related?
-
View Policies Current Attempt in Progress These transactions took place for Oriole Co. 2024 May 1 Dec. 31 Received a $7,200, 12-month, 3% note in exchange for an outstanding account receivable from...
-
Which task is performed by a book-keeper? A. Analysing the trading results B. Entering transactions in the ledger C. Preparing year-end financial statements D. Providing information for...
-
Let f(x) = (e x - 1)/x, for x 0, and f(0) = 1. Use the Taylor series for f about 0 and evaluate f(1) to find the value of
-
Find the nth-order Taylor polynomial for the following functions centered at the given point a. f(x) = e -x , n = 2, a = 0
-
Find the function r that satisfies the given conditions. 3 2t k; r(0) = i + te-*j 3k r'(t) Vi? + 4 t2 + 1
-
Paddle Petroleum has the following account balances at 12/31/15: The above properties are abandoned in 2016. Record the abandonment entry. Lease A: unproved property Lease B: proved property... Wells...
-
Aaron Energy Corporation has the following account balances at 12/31/15: At 12/31/15, Lease A is considered to be 40% impaired. Aaron Energys estimated abandonment rate of insignificant unproved...
-
Dwight Oil and Gas Company has the following information at 12/31/15. Production in 2015: Capitalized costs, plus future development costs..... Accumulated DD&A.. Proved reserves Oil. Gas. $2,000,000...
Study smarter with the SolutionInn App