Question

A glider begins its flight 1.2 mile above the ground. After 60 minutes, it is no mile above the ground. Find the change in height of the glider.If it continues to descend at this rate, how long does the entire descent last?

Answer 1

We can model the problem using the equation of a straight line:

h(t) = mt + b

Where:

m = the change in height of the glider = slope

b = Initial height

We can find m using the folling formula:

m = (h2 - h1)/(t2 - t1)

t1 = 0 min

t2 = 60 min

h2 = 0 miles

h1 = 1.2 miles

Hence:

m = (0 - 1.2)/(60- 0) = -0.02mi/min

And:

h(t) = -0.02t + 1.2

If it continues to descend at this rate, how long does the entire descent last? Well, mathematically this means:

h(t) = -0.02t + 1.2 = 0

-0.02t + 1.2 = 0

Solving for t:

Add 0.02t to both sides:

-0.02t + 1.2 + 0.02t = 0 + 0.02t

1.2 = 0.02t

Divide both sides by 0.02:

1.2/0.02 = 0.02t/0.02

60 = t

t = 60