y = xtane gx² 2v²cos²0 + Yo If 7'1"Shaquille O'Neal is at the free throw line (that is 4 feet from the point under the 10-ft rim of the basket,) and he throws the ball with the initial velocity 35 feet per second and the angle of inclination 8 = 39.25°, does he make the free throw successfully? Explain your answer in details. (Hint 7'1"=7.083ft and g = 32ft/s²) 4' 10'
y = xtane gx² 2v²cos²0 + Yo If 7'1"Shaquille O'Neal is at the free throw line (that is 4 feet from the point under the 10-ft rim of the basket,) and he throws the ball with the initial velocity 35 feet per second and the angle of inclination 8 = 39.25°, does he make the free throw successfully? Explain your answer in details. (Hint 7'1"=7.083ft and g = 32ft/s²) 4' 10'
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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![The text on the image deals with a physics problem related to projectile motion. The focus is on whether Shaquille O'Neal can make a free throw with specific initial conditions.
**Text Transcription and Explanation:**
1. **Equation Provided:**
\[
y = x \tan{\theta} - \frac{gx^2}{2v_0^2 \cos^2{\theta}} + y_0
\]
2. **Problem Statement:**
If 7'1" Shaquille O'Neal is at the free throw line (which is 4 feet from the point under the 10-ft rim of the basket), and he throws the ball with an initial velocity of 35 feet per second and an angle of inclination \(\theta = 39.25^\circ\), does he make the free throw successfully? Explain your answer.
**Hint:** 7'1" = 7.083 feet, \( g = 32 \text{ ft/s}^2 \).
3. **Given Details:**
- Height of Shaq = 7.1" = 7.083 ft
- Initial velocity \( v_0 = 35 \text{ ft/s} \)
- Angle \( \theta = 39.25^\circ \)
- Acceleration due to gravity \( g = 32 \text{ ft/s}^2 \)
4. **Solution Steps:**
- Use the equation of motion derived for projectile motion:
\[
y = x \tan{\theta} - \frac{gx^2}{2v_0^2 \cos^2{\theta}} + y_0
\]
- Inputs:
- \( y = 10 \)
- \( x = 4 \)
- Plug in the values to find:
\[
10 = 4 \tan{39.25^\circ} - \frac{16}{(35)^2 \cos^2{39.25^\circ}} + 7.083
\]
- Solve for the final equation step to see if it approximately equals 10 feet.
5. **Diagrams:**
- Depiction of Shaquille throwing a basketball and the trajectory of the ball in a parabolic path towards the basket.
- Diagram of the basketball rim at 10 feet with](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb497b8c4-4d07-4c4c-ac55-469da516b240%2F7b8859e6-b1bb-4fa7-a989-f77b39bc2e77%2Fdnd6yen_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The text on the image deals with a physics problem related to projectile motion. The focus is on whether Shaquille O'Neal can make a free throw with specific initial conditions.
**Text Transcription and Explanation:**
1. **Equation Provided:**
\[
y = x \tan{\theta} - \frac{gx^2}{2v_0^2 \cos^2{\theta}} + y_0
\]
2. **Problem Statement:**
If 7'1" Shaquille O'Neal is at the free throw line (which is 4 feet from the point under the 10-ft rim of the basket), and he throws the ball with an initial velocity of 35 feet per second and an angle of inclination \(\theta = 39.25^\circ\), does he make the free throw successfully? Explain your answer.
**Hint:** 7'1" = 7.083 feet, \( g = 32 \text{ ft/s}^2 \).
3. **Given Details:**
- Height of Shaq = 7.1" = 7.083 ft
- Initial velocity \( v_0 = 35 \text{ ft/s} \)
- Angle \( \theta = 39.25^\circ \)
- Acceleration due to gravity \( g = 32 \text{ ft/s}^2 \)
4. **Solution Steps:**
- Use the equation of motion derived for projectile motion:
\[
y = x \tan{\theta} - \frac{gx^2}{2v_0^2 \cos^2{\theta}} + y_0
\]
- Inputs:
- \( y = 10 \)
- \( x = 4 \)
- Plug in the values to find:
\[
10 = 4 \tan{39.25^\circ} - \frac{16}{(35)^2 \cos^2{39.25^\circ}} + 7.083
\]
- Solve for the final equation step to see if it approximately equals 10 feet.
5. **Diagrams:**
- Depiction of Shaquille throwing a basketball and the trajectory of the ball in a parabolic path towards the basket.
- Diagram of the basketball rim at 10 feet with
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