Explanation Given: According to special relativity, the stone’s mass depends on its velocity divided by c, and the maximum height is given by h ( c ) = c c 2 g 2 + 1 4 − c 2 g A stone tossed up vertically from ground level returns to Earth 1s later Using Newton’s laws, the stone’s maximum height is h = g 8 Einstein’s theory of special relativity reduces to Newtonian mechanics in the limit as c → ∞ . Thus, by applying the limit lim c → ∞ h ( c ) on the equation h ( c ) = c c 2 g 2 + 1 4 − c 2 g , we can find the stone’s maximum height using Einstein’s theory of special relativity. The given equation has a radical; this can be simplified by multiplying and dividing by its conjugate. After simplification, to apply limit at infinity, the infinity properties can be used. Calculations: Description lim c → ∞ h ( c ) ; Step 1: The given equation has a radical; this can be simplified by multiplying and dividing by its conjugate. h ( c ) = c c 2 g 2 + 1 4 − c 2 g = ( c c 2 / g 2 + 1 / 4 − c 2 / g ) ( c c 2 / g 2 + 1 / 4 + c 2 / g ) c c 2 / g 2 + 1 / 4 + c 2 / g Step 2: Using the algebraic identity ( a + b ) ( a − b ) = a 2 − b 2 , we get h ( c ) = ( c c 2 / g 2 + 1 / 4 ) 2 − ( c 2 / g ) 2 c c 2 / g 2 + 1 / 4 + c 2 / g = c 2 ( c 2 / g 2 + 1 / 4 ) − c 4 / g 2 c c 2 / g 2 + 1 / 4 + c 2 / g Step 3: Remove the brackets by distributing c 2 times to each term within the brackets. h ( c ) = c 4 / g 2 + c 2 / 4 − c 4 / g 2 c c 2 / g 2 + 1 / 4 + c 2 / g = c 4 / g 2 + c 2 / 4 − c 4 / g 2 c c 2 / g 2 + 1 / 4 + c 2 / g Step 4: Simplify the denominator by taking out the term c 2 g 2 that is distributed within the square-root. Since the terms is absent in the second term, it is multiplied with the inverse term g 2 c 2

4th Edition

ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topic…

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Chapter 2.7, Problem 44E

To determine

To prove:

limc→∞h(c)=g/8

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Chapter 2.7, Problem 43E

Chapter 2.7, Problem 45E

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Chapter 2 Solutions

CALCULUS W/SAPLING ACCESS >IC<

Ch. 2.1 - Prob. 1PQ Ch. 2.1 - Prob. 2PQ Ch. 2.1 - Prob. 3PQ Ch. 2.1 - Prob. 4PQ Ch. 2.1 - Prob. 1E Ch. 2.1 - Prob. 2E Ch. 2.1 - Prob. 3E Ch. 2.1 - Prob. 4E Ch. 2.1 - Prob. 5E Ch. 2.1 - Prob. 6E

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