The function h defined by h(t)=(49+4.9t)(10-t) models the height, in meters, of an object t seconds after it is dropped from a helicopter.

Question

a.) Find or approximate the time when the object hits the ground. Explain or show your reasoning

b.) From what height was the object dropped? Explain or show your reasoning

Answer 1

h(t)=(49+4.9t)(10-t)

Notice that h goes from the initial height of the helicopter down to zero.

t goes from 0 ("after it is dropped") up to the maximum t (when the object hits the ground)

Actually, it is easier to find h first (part b), so let's do that first:

At t=0,

h = (49)(10)

h = 490 m

O.K., now find maximum t (part a).

Well, at maximum t, we know that h = 0 ("hits the ground")

h(0) = (49+4.9t)(10-t)

0 = (49+4.9t)(10-t)

0 = 490 + 490t - 49t - 4.9t (remember F-I-O-L)

0 = 490 - 436.1t

-490 = -436.1t

1.12 ≅ t

Now, measuring one tenth or one hundredth of one hundredth of a second requires very special instruments (not just a stopwatch), so you should say that the object hit the ground at t=1 second.

Let's check to see how close we are:

h(1) =(49+4.9(1))(10-1)

h(1) = (49 + 4.9)(9)

h(1) = 485.1 meters

This check gave 485.1 meters instead of 490 meters. For 490 meters, being off by less than 5 meters is close enough to be called a "good estimate."