A small raindrop measuring 1.2 mm in diameter has a terminal velocity of 10.22 miles per hour. A large raindrop measuring 5.0 mm in diameter has a terminal velocity of 20.1 miles per hour. If there is a linear relationship between the diameter of a raindrop and its terminal velocity, what is the terminal velocity of a raindrop measuring 3.0 mm in diameter?
Let
x -----> the diameter in mm
y -----> terminal velocity in miles per hour
so
In this problem we have the ordered pairs
(1.2,10.22) and (5.0,20.1)
step 1
Find the slope of the linear equation
m=(20.1-10.22)/(5.0-1.2)
m=9.88/3.8
m=2.6
step 2
Find the equation of the line
y-y1=m(x-x1)
we have
m=2.6
(x1,y1)=(1.2,10.22)
substitute
y-10.22=2.6(x-1.2)
step 3
For x=3.0 mm
substitute in the expression above
y-10.22=2.6(3.0-1.2)
y-10.22=4.68
y=4.68+10.22
y=14.9
therefore
the answer is 14.9 miles per hour