If a ball is thrown into the air with a velocity of 40 ft / s, its height (in feet) after t seco

Name: Problem 13, Chapter 2: Calculus
Uploaded: 2020-04-01T03:49:32-08:00
Duration: 3 min 24 s
Channel: Bobby Barnes
Description: If a ball is thrown into the air with a velocity of 40 ft / s, its height (in feet) after t seconds is given by y=40 t-16 t^2. Find the velocity when t=2.

step 1 We're told a ball is thrown in the air with velocity of 40 feet per second, and its height can b

Question

If a ball is thrown into the air with a velocity of $40 \mathrm{ft} / \mathrm{s}$, its height (in feet) after $t$ seconds is given by $y=40 t-16 t^2$. Find the velocity when $t=2$.

   If a ball is thrown into the air with a velocity of $40 \mathrm{ft} / \mathrm{s}$, its height (in feet) after $t$ seconds is given by $y=40 t-16 t^2$. Find the velocity when $t=2$.

Calculus

James Stewart 7th Edition

Chapter 2, Problem 13

Instant Answer

Solved by Expert Bobby Barnes

04/01/2020

Step 1

We are given the height function of a ball thrown into the air: \[ y = 40t - 16t^2 \] where $ y $ is the height in feet and $ t $ is the time in seconds. We need to find the velocity of the ball at $ t = 2 $ seconds. Show more…

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If a ball is thrown into the air with a velocity of $40 \mathrm{ft} / \mathrm{s}$, its height (in feet) after $t$ seconds is given by $y=40 t-16 t^2$. Find the velocity when $t=2$.

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Key Concepts

Projectile Motion

Projectile motion deals with the motion of objects thrown into the air, where their paths are influenced largely by gravity. The equations used typically involve quadratic relationships between height and time, illustrating key principles of kinematics, including velocity and acceleration.

Differentiation

Differentiation is a fundamental operation in calculus that computes the instantaneous rate of change of a function. When applied to a position function, it yields a velocity function, enabling the analysis of motion through the application of derivative rules.

Instantaneous Velocity

Instantaneous velocity is the rate at which an object's position changes at a specific moment in time. In calculus, this concept is represented as the derivative of the position function with respect to time, providing a precise measure of speed in a given direction at any instant.

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