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Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

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BuyFindarrow_forward

Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

Vertical Motion In Exercises 57-59, assume the acceleration of the object is a ( t ) = 32 feet per second per second. (Neglect air resistance.)

With what initial velocity must an object be thrown upward (from ground level) to reach the top of the Washington Monument (approximately 550 feet)?

To determine

To calculate: The initial velocity must be object thrown upwards to reach the top of the Washington Monument (approximately 550 feet).

Explanation

Given:

The object thrown upwards (from the ground level) to reach the top of the Washington Monument (approximately 550 feet).

Formula used:

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

Calculation:

Let t=0 represent the initial time and the position of the object is y at any instant. The object thrown upwards from the ground level.

y(0)=0

Since, the acceleration due to gravity g=32 feet per second per second. So, the equation is written as,

y=32

Integrate the above equation with respect to t,

y=32dt=32t+C1

Let the initial velocity of the object is v0. Now, find the value of C1,

y(0)=32(0)+C1v0=C1

Now, the equation y is written as,

y=32t+v0

When ball reach the maximum height 550 feet its velocity is zero

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