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Assume the acceleration of the object is att)--9.8 meters per second. (Neçlect air resistance.) With what initial velocity must an object be thrown upward (from a height of 3 meters) to reach a maximurm height of 360 meters? Step 1 We want to find the initial velocity, v(0) of an object thrown upward such that the maximum of the height function t) is 360. We also assume the acceleration due to gravity is a(t) = -9.8 meters per second. First, we must find an equation for the velocity and height functions. Recall that the derivative of the velocity function is acceleration, or vtt) - a(t). This also means that v(t) is the antiderivative of the constant function a(t). Find v(). e+c The initial velocity is the velocity at time t= 0. Find the initial velocity by substituting O for t in the equation above. v(0) =

Assume the acceleration of the object is att)--9.8 meters per second. (Neçlect air resistance.) With what initial velocity must an object be thrown upward (from a height of 3 meters) to reach a maximurm height of 360 meters? Step 1 We want to find the initial velocity, v(0) of an object thrown upward such that the maximum of the height function t) is 360. We also assume the acceleration due to gravity is a(t) = -9.8 meters per second. First, we must find an equation for the velocity and height functions. Recall that the derivative of the velocity function is acceleration, or vtt) - a(t). This also means that v(t) is the antiderivative of the constant function a(t). Find v(). e+c The initial velocity is the velocity at time t= 0. Find the initial velocity by substituting O for t in the equation above. v(0) =

Calculus: Early Transcendentals
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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Assume the acceleration of the object is att) --9.8 meters per second. (Neclect air resistance.) With what initial veloaity must an object be thrown upward (from a height of 3 meters) to reach a maximurm height of 360 meters? Step 1 We want to find the initial velocity, v(0) of an object thrown upward such that the maximum of the height function t) is 360. We also assume the acceleration due to gravity is a(t) - -9.8 meters per second. First, we must find an equation for the velocity and height functions. Recall that the derivative of the velocity function is acceleration, or vtt) - a(t). This also means that v(t) is the antiderivative of the constant function a(t). Find v(). ])e + c The initial velocity is the velocity at time t=0. Find the initial velocity by substituting 0 for t in the equation above. v(0) =
Transcribed Image Text:Assume the acceleration of the object is att) --9.8 meters per second. (Neclect air resistance.) With what initial veloaity must an object be thrown upward (from a height of 3 meters) to reach a maximurm height of 360 meters? Step 1 We want to find the initial velocity, v(0) of an object thrown upward such that the maximum of the height function t) is 360. We also assume the acceleration due to gravity is a(t) - -9.8 meters per second. First, we must find an equation for the velocity and height functions. Recall that the derivative of the velocity function is acceleration, or vtt) - a(t). This also means that v(t) is the antiderivative of the constant function a(t). Find v(). ])e + c The initial velocity is the velocity at time t=0. Find the initial velocity by substituting 0 for t in the equation above. v(0) =
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