(a) Explanation Given information: The altitude (in feet) of aircraft t sec ( 0 ≤ t ≤ 8 ) after liftoff is given by, h ( t ) = 1 16 t 4 − t 3 + 4 t 2 Calculation: The aircraft’s velocity at any time t is the derivative of the given function h ( t ) with respect to t . The derivative of the function h ( t ) is, h ′ ( t ) = d d t ( 1 16 t 4 − t 3 + 4 t 2 ) = d d t ( 1 16 t 4 ) − d d t t 3 + d d t 4 t 2 ( d d x [ f ( x ) ± g ( x ) ] = d d x [ f ( x ) ] ± d d x [ g ( x ) ] ) = 1 16 d d t t 4 − d d t t 3 + (b) To determine The aircraft’s velocity when t is 0, 4, and 8. (c) To determine The expression for the aircraft’s acceleration at time t . (d) To determine The aircraft’s acceleration when t is 0, 4, and 8. (e) To determine The aircraft’s height when t is 0, 4, and 8.

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ISBN: 9781337825597

Author: Tan

Publisher: INTER CENG

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Question

Chapter 3.5, Problem 38E

(a)

To determine

The expression for the aircraft’s velocity at time t.

(b)

To determine

The aircraft’s velocity when t is 0, 4, and 8.

(c)

To determine

The expression for the aircraft’s acceleration at time t.

(d)

To determine

The aircraft’s acceleration when t is 0, 4, and 8.

(e)

To determine

The aircraft’s height when t is 0, 4, and 8.

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Chapter 3.5, Problem 37E

Chapter 3.5, Problem 39E

Chapter 3 Solutions

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The expression for the aircraft’s velocity at time t .

Solution Summary: The author calculates the aircraft's velocity at any time t as the derivative of the given function h(t).

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The expression for the aircraft’s velocity at time t.

The aircraft’s velocity when t is 0, 4, and 8.

The expression for the aircraft’s acceleration at time t.

The aircraft’s acceleration when t is 0, 4, and 8.

The aircraft’s height when t is 0, 4, and 8.

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Chapter 3 Solutions