16soln.practice1

# 16soln.practice1 - 16B Calculus Monica Vazirani Jan 24,...

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16B Calculus Monica Vazirani Jan 24, 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 0 ( t ) = s 00 ( t ) so v ( t ) = Z v 0 ( t ) dt = Z - 32 dt = - 32 t + v 0 where v 0 = v (0) the initial velocity which is unknown. Likewise s ( t ) = Z ( - 32 t + v 0 ) = - 16 t 2 + v 0 t + s 0 = - 16 t 2 + v 0 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 0 . -

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## This note was uploaded on 02/17/2009 for the course MATH NA taught by Professor Na during the Spring '09 term at UC Davis.

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16soln.practice1 - 16B Calculus Monica Vazirani Jan 24,...

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