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Unformatted text preview: 16B Calculus Francisco Santos October 15, 2007 Practice Midterm 1 SOLUTIONS Name: ID: 1. (9 points) Determine whether each statement is true (T) or false (F), then CIRCLE the appropriate response. You do not need to show work. Assume that x and y are positive. ( a ) ln( x + y ) = (ln x )(ln y ) F ( b ) ln( x 3 ) = 3(ln x ) T ( c ) e x e y = e x + y T 2. (20 points) Carlos and Jeff are playing catch by the math building. Carlos is on the ground, and Jeff is on top of MSB, 49 feet off the ground. a. With what initial velocity must Carlos toss the ball up so that Jeff can (just barely) catch it? Solution: Note, part a and b have the SAME solution up to sign. Think about why. That gives the easiest soln to part a. A longer soln is here: a ( t ) = 32 = v ( t ) = s 00 ( t ) so v ( t ) = Z v ( t ) dt = Z 32 dt = 32 t + v where v = v (0) the initial velocity which is unknown. Likewise s ( t ) = Z ( 32 t + v ) = 16 t 2 + v t + s = 16 t 2 + v t because s (0) = 0 if we start on the ground. That the ball just reaches Jeff means its maximum height is 49 . So at the time t 1 that v ( t 1 ) = 0 we also need s ( t 1 ) = 49 . That gives us 2 equations in 2 unknowns and we can solve for v . 32 t 1 + v = 0 (so t 1 = v / 32 ) 16 t 2 1 + v t 1 = 49 that is 16( v / 32) 2 + v ( v / 32) = 49 v 2 / 64 + v 2 / 32 = 49 v 2 / 64 = 49 v = ± √ 49 · 64 = ± 7 · 8 = ± 56 Since we require positive (upward) velocity, v = 56 feet/sec ....
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This note was uploaded on 06/15/2011 for the course CAL 3 taught by Professor Smith during the Spring '11 term at Arkansas State.
 Spring '11
 Smith

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