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51. An artillery specialist practicing at a firing range on a flat stretch of ground fires a shell from 1 m above the ground, with a muzzle velocity of 96 m/sec at an angle of 16° from the horizontal. Choose a coordinate system with the origin at ground level directly below the launch position. (See Example 6) a. Write parametric equations that model the path of the shell as a function of time t (in sec) after launch. b. Approximate the time required for the shell to hit the ground. Round to the nearest hundredth of a second. c. Approximate the horizontal distance that the shell travels before it hits the ground. Round to the nearest meter.

51. An artillery specialist practicing at a firing range on a flat stretch of ground fires a shell from 1 m above the ground, with a muzzle velocity of 96 m/sec at an angle of 16° from the horizontal. Choose a coordinate system with the origin at ground level directly below the launch position. (See Example 6) a. Write parametric equations that model the path of the shell as a function of time t (in sec) after launch. b. Approximate the time required for the shell to hit the ground. Round to the nearest hundredth of a second. c. Approximate the horizontal distance that the shell travels before it hits the ground. Round to the nearest meter.

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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Objective 4: Apply Parametric Equations For Exercises 47-48, an object undergoes uniform linear motion on a straight path from point A to point B in At sec. Write parametric equations over an interval I that describe the motion along the path. %3D 48. A = (10, 7), B = (-14, 1), and At = 6 sec %3D 47. A = (1, 5), B = (7, 3), and At = 2 sec %3D %3D 49. Suppose that the origin on a computer screen is in the lower left corner of the screen. A target moves along a straight line at a constant speed from point A(670, 450) to point B(250, 210) in 4 sec. (See Example 5) 50. A hospital is located 3 mi west and 4 mi north of the center of town. Suppose that a Medi-Vac helicopter flies at a constant speed from the hospital to the location of an accident 15 mi east and 20 mi south of the center of town in 15 min ( hr). Choose a coordinate system with the origin at the center of town. a. Write parametric equations to represent the target's path as a function of the time t (in sec) after the target leaves its initial position. a. Write parametric equations to represent the path of the helicopter as a function of the time t (in hr) after the helicopter leaves the hospital. b. Where is the helicopter located 10 min after leaving the hospital? b. Where is the target located 1.4 sec after motion starts? 51. An artillery specialist practicing at a firing range on a flat stretch of ground fires a shell from 1 m above the ground, with a muzzle velocity of 96 m/sec at an angle of 16° from the horizontal. Choose a coordinate system with the origin at ground level directly below the launch position. (See Example 6) 52. A golfer tees off on level ground, and hits the ball with an initial speed of 52 m/sec at an angle of 34° above the horizontal. Choose a coordinate system with the origin at the point where the ball is struck. a. Write parametric equations that model the path of the ball as a function of time t (in sec). a. Write parametric equations that model the path of the shell as a function of time t (in sec) after launch. b. For how long will the ball be in the air before it hits the ground? Round to the nearest hundredth of a second. b. Approximate the time required for the shell to hit the ground. Round to the nearest hundredth of a second. c. Approximate the horizontal distance that the shell travels before it hits the ground. Round to the c. Approximate the horizontal distance that the ball travels before it hits the ground. Round to the nearest foot. nearest meter. d. When is the shell at its maximum height? Find the exact value and an approximation to the nearest hundredth of a second. d. When is the ball at its maximum height? Find the exact value and an approxinmation to the nearest hundredth of a second. e. What is the maximum height? Round to the e. Determine the maximum height. Round to the nearest foot. nearest meter.
Transcribed Image Text:Objective 4: Apply Parametric Equations For Exercises 47-48, an object undergoes uniform linear motion on a straight path from point A to point B in At sec. Write parametric equations over an interval I that describe the motion along the path. %3D 48. A = (10, 7), B = (-14, 1), and At = 6 sec %3D 47. A = (1, 5), B = (7, 3), and At = 2 sec %3D %3D 49. Suppose that the origin on a computer screen is in the lower left corner of the screen. A target moves along a straight line at a constant speed from point A(670, 450) to point B(250, 210) in 4 sec. (See Example 5) 50. A hospital is located 3 mi west and 4 mi north of the center of town. Suppose that a Medi-Vac helicopter flies at a constant speed from the hospital to the location of an accident 15 mi east and 20 mi south of the center of town in 15 min ( hr). Choose a coordinate system with the origin at the center of town. a. Write parametric equations to represent the target's path as a function of the time t (in sec) after the target leaves its initial position. a. Write parametric equations to represent the path of the helicopter as a function of the time t (in hr) after the helicopter leaves the hospital. b. Where is the helicopter located 10 min after leaving the hospital? b. Where is the target located 1.4 sec after motion starts? 51. An artillery specialist practicing at a firing range on a flat stretch of ground fires a shell from 1 m above the ground, with a muzzle velocity of 96 m/sec at an angle of 16° from the horizontal. Choose a coordinate system with the origin at ground level directly below the launch position. (See Example 6) 52. A golfer tees off on level ground, and hits the ball with an initial speed of 52 m/sec at an angle of 34° above the horizontal. Choose a coordinate system with the origin at the point where the ball is struck. a. Write parametric equations that model the path of the ball as a function of time t (in sec). a. Write parametric equations that model the path of the shell as a function of time t (in sec) after launch. b. For how long will the ball be in the air before it hits the ground? Round to the nearest hundredth of a second. b. Approximate the time required for the shell to hit the ground. Round to the nearest hundredth of a second. c. Approximate the horizontal distance that the shell travels before it hits the ground. Round to the c. Approximate the horizontal distance that the ball travels before it hits the ground. Round to the nearest foot. nearest meter. d. When is the shell at its maximum height? Find the exact value and an approximation to the nearest hundredth of a second. d. When is the ball at its maximum height? Find the exact value and an approxinmation to the nearest hundredth of a second. e. What is the maximum height? Round to the e. Determine the maximum height. Round to the nearest foot. nearest meter.
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