16x² 77.9 45 (45)² horizontal distance of the golf ball from the point of impact. What is the horizontal distance of the golf ball from the point of impact when the ball is at its maximum height? What is the maximum height obtained by the golf ball? A golf ball is struck by a 60-degree golf club at an initial velocity of 90 feet per second. The height of the golf ball in feet is given by the quadratic function h(x) = - C The horizontal distance of the golf ball from the point of impact when the ball is at its maximum height is (Round to two decimal places as needed.) feet. + -x, where x is the
16x² 77.9 45 (45)² horizontal distance of the golf ball from the point of impact. What is the horizontal distance of the golf ball from the point of impact when the ball is at its maximum height? What is the maximum height obtained by the golf ball? A golf ball is struck by a 60-degree golf club at an initial velocity of 90 feet per second. The height of the golf ball in feet is given by the quadratic function h(x) = - C The horizontal distance of the golf ball from the point of impact when the ball is at its maximum height is (Round to two decimal places as needed.) feet. + -x, where x is the
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Projectile Motion and Quadratic Functions
In this educational exercise, we explore the motion of a golf ball struck by a golf club.
#### Problem Statement:
A golf ball is struck by a 60-degree golf club at an initial velocity of 90 feet per second. The height of the golf ball in feet is given by the quadratic function:
\[ h(x) = -\frac{16x^2}{(45)^2} + \frac{77.9}{45}x \]
where \( x \) is the horizontal distance of the golf ball from the point of impact.
**Questions:**
1. What is the horizontal distance of the golf ball from the point of impact when the ball is at its maximum height?
2. What is the maximum height obtained by the golf ball?
#### Solving the Quadratic Function:
To find the horizontal distance when the ball is at its maximum height, we need to determine the vertex of the quadratic function.
**1. Horizontal Distance at Maximum Height:**
The quadratic function is of the form:
\[ h(x) = ax^2 + bx + c \]
The horizontal distance at the vertex (maximum height) is given by:
\[ x = -\frac{b}{2a} \]
In our function:
\[ a = -\frac{16}{(45)^2} \]
\[ b = \frac{77.9}{45} \]
Plugging in these values:
\[ x = -\frac{\frac{77.9}{45}}{2 \times -\frac{16}{2025}} \]
\[ x = \frac{\frac{77.9}{45}}{\frac{32}{2025}} \]
\[ x = \frac{77.9 \times 2025}{45 \times 32} \]
\[ x = \frac{77.9 \times 45}{32} \]
\[ x = 75.10 \]
So, the horizontal distance of the golf ball from the point of impact when the ball is at its maximum height is approximately **75.10 feet**.
(Note: There's a blank square indicating where students would input their answer.)
This type of problem is essential for understanding projectile motion and the applications of quadratic functions in real-world scenarios. It provides a practical example of how math principles are applied in sports and physics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ae5415e-4394-4e91-afd5-48b91660ab22%2Fbf686e68-0fbf-4065-8224-83dd01125ee8%2Fdmc3ws2_processed.png&w=3840&q=75)
Transcribed Image Text:### Projectile Motion and Quadratic Functions
In this educational exercise, we explore the motion of a golf ball struck by a golf club.
#### Problem Statement:
A golf ball is struck by a 60-degree golf club at an initial velocity of 90 feet per second. The height of the golf ball in feet is given by the quadratic function:
\[ h(x) = -\frac{16x^2}{(45)^2} + \frac{77.9}{45}x \]
where \( x \) is the horizontal distance of the golf ball from the point of impact.
**Questions:**
1. What is the horizontal distance of the golf ball from the point of impact when the ball is at its maximum height?
2. What is the maximum height obtained by the golf ball?
#### Solving the Quadratic Function:
To find the horizontal distance when the ball is at its maximum height, we need to determine the vertex of the quadratic function.
**1. Horizontal Distance at Maximum Height:**
The quadratic function is of the form:
\[ h(x) = ax^2 + bx + c \]
The horizontal distance at the vertex (maximum height) is given by:
\[ x = -\frac{b}{2a} \]
In our function:
\[ a = -\frac{16}{(45)^2} \]
\[ b = \frac{77.9}{45} \]
Plugging in these values:
\[ x = -\frac{\frac{77.9}{45}}{2 \times -\frac{16}{2025}} \]
\[ x = \frac{\frac{77.9}{45}}{\frac{32}{2025}} \]
\[ x = \frac{77.9 \times 2025}{45 \times 32} \]
\[ x = \frac{77.9 \times 45}{32} \]
\[ x = 75.10 \]
So, the horizontal distance of the golf ball from the point of impact when the ball is at its maximum height is approximately **75.10 feet**.
(Note: There's a blank square indicating where students would input their answer.)
This type of problem is essential for understanding projectile motion and the applications of quadratic functions in real-world scenarios. It provides a practical example of how math principles are applied in sports and physics.
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