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). b. For how long will the ball be in the air before it hits the ground? Round to the nearest hundredth of a second. c. Approximate the horizontal distance that the ball travels before it hits the ground. Round to the nearest foot.
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). b. For how long will the ball be in the air before it hits the ground? Round to the nearest hundredth of a second. c. Approximate the horizontal distance that the ball travels before it hits the ground. Round to the nearest foot.
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**Chapter 10: Analytic Geometry - Page 990**
**Exercises 43-46: Parametric Equations on a Restricted Interval**
For each exercise, write parametric equations on a restricted interval for \( t \) to define the given graph:
43. Graph shows the right half of an ellipse.
44. Graph depicts a line segment.
45. Graph displays the right half of an ellipse, similar to exercise 43.
46. Graph illustrates the top branch of a hyperbola.
**Objective 4: Apply Parametric Equations**
**Exercises 47-48:** An object undergoes uniform linear motion on a straight path from point \( A \) to point \( B \) in \( \Delta t \) seconds. Write parametric equations over an interval \( I \) that describe the motion along the path.
47. \( A = (1, 5) \), \( B = (7, 3) \), and \( \Delta t = 2 \) sec.
48. \( A = (10, 7) \), \( B = (-14, 1) \), and \( \Delta t = 6 \) sec.
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**Problem 49: Computer Screen Target Motion**
A target moves along a straight line at a constant speed from point \( A(670, 450) \) to point \( B(250, 210) \) in 4 seconds. Write parametric equations to represent the target’s path as a function of time \( t \).
a. Find the location of the target 1.4 seconds after motion starts.
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**Problem 51: Artillery Projectile Motion**
An artillery shell is fired from a height of 1 m above the ground with a muzzle velocity of 96 m/sec at an angle of 16° from the horizontal.
a. Write parametric equations for the shell's path as a function of time \( t \).
b-e. Calculate various aspects of the projectile motion including time of flight, horizontal distance, maximum height, and determine the maximum height reached.
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**Problem 50: Helicopter Flight Path**
A hospital is located 3 mi west and 4 mi north of a town center. A helicopter flies from the hospital to an accident site located 15 mi east and 20 mi south of the town center in 15 minutes. Write parametric equations for the helicopter's path and find its position after 10 minutes.
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