16soln.practice1

16soln.practice1 - 16B Calculus Francisco Santos Practice...

This preview shows pages 1–3. Sign up to view the full content.

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 ( t ) so v ( t ) = v ( t ) dt = - 32 dt = - 32 t + v 0 where v 0 = v (0) the initial velocity which is unknown. Likewise s ( t ) = ( - 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 . - 32 t 1 + v 0 = 0 (so t 1 = v 0 / 32 ) - 16 t 2 1 + v 0 t 1 = 49 that is - 16( v 0 / 32) 2 + v 0 ( v 0 / 32) = 49 - v 2 0 / 64 + v 2 0 / 32 = 49 v 2 0 / 64 = 49 v 0 = ± 49 · 64 = ± 7 · 8 = ± 56 Since we require positive (upward) velocity, v 0 = 56 feet/sec . b. If Jeff then drops the ball off the roof, with what velocity will it hit the ground?

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Name: ID: 2 Solution: Now at t = 0 we start on the roof with 0 velocity, so v ( t ) = - 32 t + 0 = - 32 t s ( t
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern