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hw2_p1 - v = dx/dt and the solution you found for v to...

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MAT22B–1: HOMEWORK 2, Part 1 Do problems #21,30,32 in Section 2.2 and the following problem: 1. A rocket sled going at a speed of 150 mi/hr is slowed by a channel of water. During the braking process, the acceleration is a = - μv, where v is the velocity and μ is a constant. Let t be time in hours and x be distance in miles. (a) Use the relation dv/dt = v ( dv/dx ) to write the equation of motion for the sled in terms of v and x. (NOTE: a = dv/dt. ) (b) Solve for v. (c) If it requires a distance of 2000 ft to slow the sled to 15 mi/hr, determine the value of μ. (NOTE: There are 5280 ft in a mile). (d) Use the fact
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Unformatted text preview: v = dx/dt and the solution you found for v to solve for x in terms of t. (Hint: Remember that at time t = 0 the position of the sled is x = 0 . So this part of the problem amounts to solving an initial valued problem dx/dt = f ( x ) , with the initial condition x (0) = 0. The right hand side of the equation is a function that does not depend explicitly on t ). (e) Use the solution you found in (d) to find the time τ required to slow the sled to 15 mi/hr. (Hint: When the sled is slowed to 15 mi/hr, its position is at 2000 ft). 1...
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