Program Explanation Given information: The aluminized sail provides a constant acceleration of 0.001 g = 0 .0098 m / s 2 . The spacecraft starts from rest at time t = 0 and the velocity of the projectile fired is the one tenth of c = 3 × 10 8 m / s . Calculation: The constant acceleration is 0.001 g = 0 .0098 m/s 2 . The acceleration can be defined as, a ( t ) = d v d t = 0.0098 Now, solve the differential equation to obtain the value of v ( t ) by integrating both sides of the equation. v ( t ) = ∫ 0.0098 d t = 0.0098 t + C Therefore, the velocity function is v ( t ) = 0.0098 t + C . The initial velocity is v 0 = 0 . Now, substitute 0 for t in equation v ( t ) = 9.8 t + C to obtain the initial velocity. v ( 0 ) = 0.0098 ( 0 ) + C v ( 0 ) = C Now, substitute 0 for v ( 0 ) to obtain the value of constant C. v ( 0 ) = C C = 0 Therefore, the particular velocity function is v ( t ) = 0.0098 t . The velocity can be defined as, v ( t ) = d y d t = 0.0098 t The position function can be defined as, y ( t ) = ∫ 0.0098 t d t = 0.0098 t 2 + C Therefore, the position function is y ( t ) = 0.0098 t 2 + C . Now, substitute 0 for t in position function to obtain the value of initial position. y ( 0 ) = 0.0098 ( 0 ) 2 + C y ( 0 ) = C Now, substitute 0 for y ( 0 ) to obtain the value of constant C

5th Edition

ISBN: 9780100802452

Author: Calvis

Publisher: YUZU

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Question

Chapter 1.2, Problem 43P

Program Plan Intro

To calculate: The time to catch up with the projectile by the spacecraft and also the distance travelled by it.

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Chapter 1.2, Problem 42P

Chapter 1.2, Problem 44P

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Chapter 1 Solutions

EBK DIFFERENTIAL EQUATIONS

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Knowledge Booster

The time to catch up with the projectile by the spacecraft and also the distance travelled by it.

Solution Summary: The author calculates the time to catch up with the projectile by the spacecraft and also the distance travelled by it.

To calculate: The time to catch up with the projectile by the spacecraft and also the distance travelled by it.

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Chapter 1 Solutions