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.