A ball is thrown vertically upward from a height of 6 feet with an initial velocity of 80 ft/sec. The height (in feet) of the ball at t seconds is given by s(t) = 6 + 80t - 16t².
A ball is thrown vertically upward from a height of 6 feet with an initial velocity of 80 ft/sec. The height (in feet) of the ball at t seconds is given by s(t) = 6 + 80t - 16t².
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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Using the information given in the image, find:
d) the acceleration at any time (t)
e) when it will hit the ground
f) the velocity at which it will hit the ground
![**Problem Description:**
A ball is thrown vertically upward from a height of 6 feet with an initial velocity of 80 feet per second (ft/sec). The height of the ball at \( t \) seconds is given by the function:
\[ s(t) = 6 + 80t - 16t^2 \]
where:
- \( s(t) \) is the height of the ball in feet after \( t \) seconds,
- \( t \) represents the time in seconds.
**Function Explanation:**
- **Initial Height (6 feet):** When \( t = 0 \), the height is 6 feet.
- **Initial Velocity (80 ft/sec):** The term \( 80t \) represents the effect of the initial upward velocity on the height.
- **Gravity (\(-16t^2\)):** The term \(-16t^2\) accounts for the effect of gravity slowing the ball's ascent, stopping it at the peak, and then accelerating its descent back down.
This quadratic function combines these three aspects to describe the motion of the ball through time.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffe7817cb-5274-4434-90ec-13ab480c973d%2Fedc05481-b80d-40b4-9d32-d67caf827ec8%2F65j2kon_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Description:**
A ball is thrown vertically upward from a height of 6 feet with an initial velocity of 80 feet per second (ft/sec). The height of the ball at \( t \) seconds is given by the function:
\[ s(t) = 6 + 80t - 16t^2 \]
where:
- \( s(t) \) is the height of the ball in feet after \( t \) seconds,
- \( t \) represents the time in seconds.
**Function Explanation:**
- **Initial Height (6 feet):** When \( t = 0 \), the height is 6 feet.
- **Initial Velocity (80 ft/sec):** The term \( 80t \) represents the effect of the initial upward velocity on the height.
- **Gravity (\(-16t^2\)):** The term \(-16t^2\) accounts for the effect of gravity slowing the ball's ascent, stopping it at the peak, and then accelerating its descent back down.
This quadratic function combines these three aspects to describe the motion of the ball through time.
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