   Chapter 5, Problem 19RE ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Vertical Motion An object is projected upward from the ground with an initial velocity of 80 feet per second. Express the height s (in feet) of the object as a function of the time t (in seconds). How long will the object be in the air? (Use s′′(t) = −32 feet per second per second as the acceleration due to gravity and neglect air resistance.)

To determine

To calculate: The fight time for an object that project upward from the ground within initial velocity of 80 feet per second that satisfied differential equation s(t)=32 feet per second.

Explanation

Given Information:

The provided differential equation s(t)=32 feet per second.

The initial condition s(0)=0 and v(0)=80

Formula used:

The rate of change of velocity describes the acceleration,

a(t)=dv(t)dt=dv(t)dt

The rate of change of displacement describes the velocity,

v(t)=ds(t)dt

The power rule of integrals:

undu=un+1n+1+C (for n1)

Here, u is function of x.

The property of Intro-differential:

df(x)dxdx=f(x)

Calculation:

Consider the derivative:

s(t)=32

The rate of change of velocity describes the acceleration,

dv(t)dt=32

Apply, integration on both sides and apply Intro-differential property:

dv(t)dtdt=(32)dt+Cv(t)=32t+C

Substitute, 80 for v(0) and 0 for t

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