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PROBLEM-SOLVING STRATEGY 4.1 Projectile motion problems Learning Goal: A rock thrown with speed 7.00 m/s and launch angle 30.0° (above the horizontal) travels a horizontal distance of d = 19.5 m before hitting the ground. From what height was the rock thrown? Use the value g = 9.800 m/s² for the free-fall acceleration. MODEL: Is it reasonable to ignore air resistance? If so, use the projectile motion model. VISUALIZE: Establish a coordinate system with the x-axis horizontal and the y-axis vertical. Define symbols and identify what the problem is trying to find. For a launch at angle 0, the initial velocity components are Vix = vocose and Viy = vosinė. SOLVE: The acceleration is known: ax = = 0 and ay = −g. Thus, the problem becomes one of two-dimensional kinematics. The kinematic equations are Horizontal xfxivix At Vfx = Vix = constant Vertical Yf = Yi + Viy▲t — —½³g(At)², - Vfy = Viy - gat At is the same for the horizontal and vertical components of the motion. Find At from one component, and then use that value for the other component. REVIEW: Check that your result has the correct units and significant figures, is reasonable, and answers the question. Part B As stated in the strategy, choose a coordinate system where the x axis is horizontal and the y axis is vertical. Note that in the strategy, the y component of the projectile's acceleration, ay, is taken to be negative. This implies that the positive y axis is upward. Use the same convention for your y axis, and take the positive x axis to be to the right. Where you choose your origin doesn't change the answer to the question, but choosing an origin can make a problem easier to solve (even if only a bit). Usually it is nice if the majority of the quantities you are given and the quantity you are trying to solve for take positive values relative to your chosen origin. Given this goal, what location for the origin of the coordinate system would make this problem easiest? At the peak of the trajectory At ground level below the point where the rock is launched At the point where the rock strikes the ground At ground level below the peak of the trajectory At the point where the rock is released

PROBLEM-SOLVING STRATEGY 4.1 Projectile motion problems Learning Goal: A rock thrown with speed 7.00 m/s and launch angle 30.0° (above the horizontal) travels a horizontal distance of d = 19.5 m before hitting the ground. From what height was the rock thrown? Use the value g = 9.800 m/s² for the free-fall acceleration. MODEL: Is it reasonable to ignore air resistance? If so, use the projectile motion model. VISUALIZE: Establish a coordinate system with the x-axis horizontal and the y-axis vertical. Define symbols and identify what the problem is trying to find. For a launch at angle 0, the initial velocity components are Vix = vocose and Viy = vosinė. SOLVE: The acceleration is known: ax = = 0 and ay = −g. Thus, the problem becomes one of two-dimensional kinematics. The kinematic equations are Horizontal xfxivix At Vfx = Vix = constant Vertical Yf = Yi + Viy▲t — —½³g(At)², - Vfy = Viy - gat At is the same for the horizontal and vertical components of the motion. Find At from one component, and then use that value for the other component. REVIEW: Check that your result has the correct units and significant figures, is reasonable, and answers the question. Part B As stated in the strategy, choose a coordinate system where the x axis is horizontal and the y axis is vertical. Note that in the strategy, the y component of the projectile's acceleration, ay, is taken to be negative. This implies that the positive y axis is upward. Use the same convention for your y axis, and take the positive x axis to be to the right. Where you choose your origin doesn't change the answer to the question, but choosing an origin can make a problem easier to solve (even if only a bit). Usually it is nice if the majority of the quantities you are given and the quantity you are trying to solve for take positive values relative to your chosen origin. Given this goal, what location for the origin of the coordinate system would make this problem easiest? At the peak of the trajectory At ground level below the point where the rock is launched At the point where the rock strikes the ground At ground level below the peak of the trajectory At the point where the rock is released

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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PROBLEM-SOLVING STRATEGY 4.1 Projectile motion problems Learning Goal: A rock thrown with speed 7.00 m/s and launch angle 30.0° (above the horizontal) travels a horizontal distance of d = 19.5 m before hitting the ground. From what height was the rock thrown? Use the value g = 9.800 m/s² for the free-fall acceleration. MODEL: Is it reasonable to ignore air resistance? If so, use the projectile motion model. VISUALIZE: Establish a coordinate system with the x-axis horizontal and the y-axis vertical. Define symbols and identify what the problem is trying to find. For a launch at angle 0, the initial velocity components are Vix = vocose and Viy = vosinė. SOLVE: The acceleration is known: ax = = 0 and ay = −g. Thus, the problem becomes one of two-dimensional kinematics. The kinematic equations are Horizontal xfxivix At Vfx = Vix = constant Vertical Yf = Yi + Viy▲t — —½³g(At)², - Vfy = Viy - gat At is the same for the horizontal and vertical components of the motion. Find At from one component, and then use that value for the other component. REVIEW: Check that your result has the correct units and significant figures, is reasonable, and answers the question.
Transcribed Image Text:PROBLEM-SOLVING STRATEGY 4.1 Projectile motion problems Learning Goal: A rock thrown with speed 7.00 m/s and launch angle 30.0° (above the horizontal) travels a horizontal distance of d = 19.5 m before hitting the ground. From what height was the rock thrown? Use the value g = 9.800 m/s² for the free-fall acceleration. MODEL: Is it reasonable to ignore air resistance? If so, use the projectile motion model. VISUALIZE: Establish a coordinate system with the x-axis horizontal and the y-axis vertical. Define symbols and identify what the problem is trying to find. For a launch at angle 0, the initial velocity components are Vix = vocose and Viy = vosinė. SOLVE: The acceleration is known: ax = = 0 and ay = −g. Thus, the problem becomes one of two-dimensional kinematics. The kinematic equations are Horizontal xfxivix At Vfx = Vix = constant Vertical Yf = Yi + Viy▲t — —½³g(At)², - Vfy = Viy - gat At is the same for the horizontal and vertical components of the motion. Find At from one component, and then use that value for the other component. REVIEW: Check that your result has the correct units and significant figures, is reasonable, and answers the question.
Part B As stated in the strategy, choose a coordinate system where the x axis is horizontal and the y axis is vertical. Note that in the strategy, the y component of the projectile's acceleration, ay, is taken to be negative. This implies that the positive y axis is upward. Use the same convention for your y axis, and take the positive x axis to be to the right. Where you choose your origin doesn't change the answer to the question, but choosing an origin can make a problem easier to solve (even if only a bit). Usually it is nice if the majority of the quantities you are given and the quantity you are trying to solve for take positive values relative to your chosen origin. Given this goal, what location for the origin of the coordinate system would make this problem easiest? At the peak of the trajectory At ground level below the point where the rock is launched At the point where the rock strikes the ground At ground level below the peak of the trajectory At the point where the rock is released
Transcribed Image Text:Part B As stated in the strategy, choose a coordinate system where the x axis is horizontal and the y axis is vertical. Note that in the strategy, the y component of the projectile's acceleration, ay, is taken to be negative. This implies that the positive y axis is upward. Use the same convention for your y axis, and take the positive x axis to be to the right. Where you choose your origin doesn't change the answer to the question, but choosing an origin can make a problem easier to solve (even if only a bit). Usually it is nice if the majority of the quantities you are given and the quantity you are trying to solve for take positive values relative to your chosen origin. Given this goal, what location for the origin of the coordinate system would make this problem easiest? At the peak of the trajectory At ground level below the point where the rock is launched At the point where the rock strikes the ground At ground level below the peak of the trajectory At the point where the rock is released
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