11) A ball is thrown directly upward from a height of 6 ft with an initial velocity of 20 ft/sec The function s(t)=-16r² +20t+6 gives the height of the ball t seconds after it has been thrown. Determine the time at which the ball reaches its maximum height, and find the maximum height.
11) A ball is thrown directly upward from a height of 6 ft with an initial velocity of 20 ft/sec The function s(t)=-16r² +20t+6 gives the height of the ball t seconds after it has been thrown. Determine the time at which the ball reaches its maximum height, and find the maximum height.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Exercise 11: Determining Maximum Height of a Projectile**
A ball is thrown directly upward from a height of 6 feet with an initial velocity of 20 feet per second. The function \( s(t) = -16t^2 + 20t + 6 \) describes the height of the ball \( t \) seconds after it has been thrown.
**Tasks:**
1. Determine the time at which the ball reaches its maximum height.
2. Find the maximum height of the ball.
**Explanation:**
The function \( s(t) = -16t^2 + 20t + 6 \) is a quadratic equation in the form \( at^2 + bt + c \), where:
- \( a = -16 \)
- \( b = 20 \)
- \( c = 6 \)
To find the time at which the maximum height is reached, use the vertex formula for a parabola:
\[ t = -\frac{b}{2a} \]
Substitute the values of \( a \) and \( b \) to determine \( t \).
Once \( t \) is found, substitute it back into \( s(t) \) to find the maximum height.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa9b6bffb-8ef6-4694-8a09-d11b0287d557%2Fc9b4dcff-47e6-41d3-82f8-b2bf89084e7c%2Fleobuy_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Exercise 11: Determining Maximum Height of a Projectile**
A ball is thrown directly upward from a height of 6 feet with an initial velocity of 20 feet per second. The function \( s(t) = -16t^2 + 20t + 6 \) describes the height of the ball \( t \) seconds after it has been thrown.
**Tasks:**
1. Determine the time at which the ball reaches its maximum height.
2. Find the maximum height of the ball.
**Explanation:**
The function \( s(t) = -16t^2 + 20t + 6 \) is a quadratic equation in the form \( at^2 + bt + c \), where:
- \( a = -16 \)
- \( b = 20 \)
- \( c = 6 \)
To find the time at which the maximum height is reached, use the vertex formula for a parabola:
\[ t = -\frac{b}{2a} \]
Substitute the values of \( a \) and \( b \) to determine \( t \).
Once \( t \) is found, substitute it back into \( s(t) \) to find the maximum height.
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