In tennis a lob can be used to buy time to get into position. The approximate height s (feet) for a tennis ball that is hit at upward at v,ft/sec from a height of soft is modeled by s=-16t² + vt + So If the ball is hit at 55 feet per second from a height of 5.2 feet, approximately how long will the tennis ball be in the air before it strikes the ground? (Round your answer to 2 decimal places)
In tennis a lob can be used to buy time to get into position. The approximate height s (feet) for a tennis ball that is hit at upward at v,ft/sec from a height of soft is modeled by s=-16t² + vt + So If the ball is hit at 55 feet per second from a height of 5.2 feet, approximately how long will the tennis ball be in the air before it strikes the ground? (Round your answer to 2 decimal places)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Title: Calculating the Time a Tennis Ball is in the Air Using Physics**
**Introduction:**
In tennis, a lob can be used to buy time to get into position. Understanding the motion of the ball can help you strategize better. The following model helps us determine the approximate height \( s \) (in feet) for a tennis ball hit upward at \( v_0 \) ft/sec from a height of \( s_0 \) ft.
**Mathematical Model:**
\[ s = -16t^2 + v_0 t + s_0 \]
Where:
- \( s \) is the height of the ball at time \( t \) seconds,
- \( v_0 \) is the initial velocity (in ft/sec) at which the ball is hit,
- \( s_0 \) is the initial height (in feet) from which the ball is hit,
- \( t \) is the time in seconds.
**Example Problem:**
*Given:*
- The initial velocity \( v_0 \) is 55 ft/sec,
- The initial height \( s_0 \) is 5.2 feet.
*Task:*
Calculate the time \( t \) the tennis ball will be in the air before it strikes the ground. Round your answer to two decimal places.
**Step-by-Step Solution:**
1. **Set up the equation:**
Given \( s = 0 \) (when the ball hits the ground), the equation becomes:
\[ 0 = -16t^2 + 55t + 5.2 \]
2. **Solve the quadratic equation:**
Apply the quadratic formula \( t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where:
- \( a = -16 \),
- \( b = 55 \),
- \( c = 5.2 \).
**Calculate the discriminant:**
\[ b^2 - 4ac = 55^2 - 4(-16)(5.2) \]
\[ = 3025 + 332.8 \]
\[ = 3357.8 \]
**Find the roots:**
\[ t = \frac{-55 \pm \sqrt{3357.8}}{2(-16)} \]
**Solving for the roots yields:**
\[ t = \frac{-55 + 57.95}{](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F70fe4f99-9e69-4bef-afe6-80d54e8903ee%2Fb24c25a1-ef2b-4966-a80c-30abb0e9b1d2%2Fvxgznrr_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Calculating the Time a Tennis Ball is in the Air Using Physics**
**Introduction:**
In tennis, a lob can be used to buy time to get into position. Understanding the motion of the ball can help you strategize better. The following model helps us determine the approximate height \( s \) (in feet) for a tennis ball hit upward at \( v_0 \) ft/sec from a height of \( s_0 \) ft.
**Mathematical Model:**
\[ s = -16t^2 + v_0 t + s_0 \]
Where:
- \( s \) is the height of the ball at time \( t \) seconds,
- \( v_0 \) is the initial velocity (in ft/sec) at which the ball is hit,
- \( s_0 \) is the initial height (in feet) from which the ball is hit,
- \( t \) is the time in seconds.
**Example Problem:**
*Given:*
- The initial velocity \( v_0 \) is 55 ft/sec,
- The initial height \( s_0 \) is 5.2 feet.
*Task:*
Calculate the time \( t \) the tennis ball will be in the air before it strikes the ground. Round your answer to two decimal places.
**Step-by-Step Solution:**
1. **Set up the equation:**
Given \( s = 0 \) (when the ball hits the ground), the equation becomes:
\[ 0 = -16t^2 + 55t + 5.2 \]
2. **Solve the quadratic equation:**
Apply the quadratic formula \( t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where:
- \( a = -16 \),
- \( b = 55 \),
- \( c = 5.2 \).
**Calculate the discriminant:**
\[ b^2 - 4ac = 55^2 - 4(-16)(5.2) \]
\[ = 3025 + 332.8 \]
\[ = 3357.8 \]
**Find the roots:**
\[ t = \frac{-55 \pm \sqrt{3357.8}}{2(-16)} \]
**Solving for the roots yields:**
\[ t = \frac{-55 + 57.95}{
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