   Chapter 4.1, Problem 62E

Chapter
Section
Textbook Problem

Vertical Motion In Exercises 60-62, assume the acceleration of the object is a ( t ) = − 9.8 meters per second per second. (Neglect air resistance.)Grand CanyonThe Grand Canyon is 1800 meters deep at its deepest point. A rock is dropped from the rim above this point. How long will it take the rock to hit the canyon floor? To determine

To calculate: The time taken by the rock to hit the canyon floor, if Grand Canyon is 1800 meters deep.

Explanation

Given:

The Grand Canyon is 1800 meters deep. A rock is dropped from the rim above this point.

Formula used:

Integration, xndx=xn+1n+1+C.

Calculation:

Let t=0 represent the initial time and the position of the rock is y at any instant. A rock is dropped from the rim above this point.

y(0)=1800

The initial height of the rock is 1800 meter. So,

y(0)=1800

Since, the acceleration due to gravity g=9.8 meter per second per second. So, the equation is written as,

y=9.8

Integrate the above equation with respect to t,

y=9.8dt=9.8t+C1

Let the initial velocity of the object is y(0)=0. Now, find the value of C1,

y(0)=9.8(0)+C10=C1

Now, the equation y is written as,

y=9

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