4 and 5 A snail is crawling in a straight line and at a cons

#4 and #5

A snail is crawling in a straight line and at a constant rate across the xy-plane. When first observed, the snail is at the point with coordinates (-2, 4). 1 minute later the snail is at the point with coordinates (3, 3). Give coordinates of the location of the snail 2 minutes before the first observation. Give an expression for both the x coordinate and the y coordinate of the snail t minutes after the first observation. Give a set of parametric equations for a line through the points (1, 7) and (3, 1).

Solution

4) First point ( -2, 4)

second point (3,3)

slope w.r.t time = deltax/detla time= (3- (-2))/1 = 5 units/min

So, x(t) = 5t

deltax/detla time= ( 3-4)/(1) = -1 units/min

y(t) = -t

Position two minutes (x, y) before it was at (-2, 4)

So, delta(x)/delta(t) = 5units/min

So, (-2 -x)/2 = 5---> -2-x = 10

x = -12

delta(y)/delta(t) = -1units/min

(4 -y)/2 =-1 ---> 4-y =-2

y = 6

So, it was at ( -12 ,6)