Quiz 4 Intermediate Calc I Spring 2005

You may consult the text and work together.
1) 1 pt, 2) 2pts 3) 2pts 4) 1 pt

Warning: if you plot the vector (1,3) with the tail at (2,7)
  this means you start at (1,3) you move 2 to the right and
  7 up, so that the tip ends up at (3,10). 


1) Find the projection of (4,5) on (1,-1).
    plot the picture to check your answer.  Be sure to
    draw the line through (1, -1) and then find the line
    perpendicular to that line which hits (4,5).  The
    projection is a vector from (0,0) to the intersection
    of the two lines.

2)  Let r(t)=( tcos(t), tsin(t) )
    Plot r(pi/2)
    Find r'(t) at t=pi/2 and plot it with the tail at r(pi/2)
    Find r''(t) at t=pi/2 and plot it with the tail at r(pi/2).

3) Let r(t)=(3cos(t), 3sin(t), 4t).  
   You do not need to plot this.  It is a helix.

   Find r'(t)

   Show the speed of r is constant = 5

   Find r''(t) 

   Check r''(t) is perpendicular to r'(t)  

      This always happens when the speed is constant.

4)  Suppose r(t) is a function whose 
       velocity at t=0 is r'(0)= (3,4) 
    and whose 
       acceleration at t=0 is r''(0)= (14,2)
    find the tangential acceleration.