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)
-
Explain why franchising is an increasingly popular route to business ownership. Who are the key parties in a franchise relationship?
-
Sampson Company uses a job order cost system with overhead applied to products based on direct labor hours. Based on previous history, the company estimated its total overhead for the coming year...
-
Based on the design, briefly discuss the data collection procedures to be used. Be sure to include the area rea of focus and targeted sample as part of these procedures. Develop a hypothetical...
-
During July 2014, Micanopy, Inc., sold 500 units of its product Empire for $8,000. The following units were available: A sale of 500 units was made after purchase 3. Of the units sold, 200 came from...
-
Simplify the given expression and write the answer with only positive exponents. -113 P 3/7 7 3 54x y z 2 w) 3) (w + 2) (3w + w 4 2 (-3x +7x+8)= (x * + 7x *-12x-1) - 5 27-7-28 20-x-22 712-24-8...
-
In preparing for next year, Tony Freedman has hired two employees to work on an hourly basis assisting with some troubleshooting and repair work. Assume the following details: a. The following...
-
Consider a gas with N=1023 molecules. Initially, the gas is contained in one half of a box, but eventually it is allowed to fill the remaining half. 1. Compute the change of entropy by counting the...
-
How does the direction of intra-entity transfers (resulting in intra-entity gross profit in inventories) affect the computation of the noncontrolling interest's share of consolidated net income Both...
-
Infinity Bank has the following balance sheet. Assets Amount Liabilities and Equity Amount ($million) Treasury notes 20 Deposits ($million) 150 Local government bonds 30 Floating-rate notes 25...
-
A child is spinning a rock at the end of a 2-foot rope at the rate of 180 revolutions per minute (rpm ). Find the linear speed of the rock when it is released.
-
As the Compliance Officer (CO) for Centennial Health (CH), you've just identified a "Cup Agreement" launched offering physicians free urine cups for those practices that signed up. With this...
-
Scenario: Henri and Lila are about to close on their new home. You are a sales agent for the clients and have been asked by them to review the closing documents for accuracy. You find three errors on...
-
#4 4. Use the method of exhaustion to prove that for all integers \( m \) between 30 and 40 inclusive (that is for \( 30 \leq m \leq 40 \) ), if \( m \) is even and then \( m \) can be written as a...
-
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
-
A landlord appeals and a tenant cross-appeals a district court ruling affirming in part and reversing in part a small claims court decision in a residential landlordtenant dispute. This is a case...
-
Norman Eastwood owns and lives in a single-family home with his wife (the Property). The Property is located in the Willow Bend Lakes Community in Plano, Texas. The Willow Bend Lakes Community is...
-
20 East 67th Street Associates LLC (Landlord) is the owner of a seven-story residential property located at 20 East 67th Street in Manhattan, New York (the Property). On January 2, 2019, Emily Jerome...
Smart Networking Attract A Following In Person And Online 1st Edition - ISBN: 0071602941 - Free Book
Study smarter with the SolutionInn App