Question

1. 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. Find or approximate the time when the object hits the ground. Explain your method.
2.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.
From what height is the object dropped? Explain how you know.

Answer 1

Answer:

Step-by-step explanation:

Let's FOIL this out and get it into standard form. That gives us:

$h(t)=-4.9t^2+490$ For #1, then:

The height of something when it is on the ground is 0; that means that the h(t) is 0. This allows us to factor the quadratic and solve for t:

$-4.9t^2=-490$ and divide both sides by 4.9 to get

$t^2=100$ so

t = 10. Notice that one of the factors for that quadratic is 10 - t. That factor represents the time it takes to hit the ground. So you might ask why, then, we FOILed this out in the first place if the answer was ight in front of our noses. The reason is becase of #2 that is asking us what the initial height of the object was. That is found in the standard form...in the constant in particular. The initial height is 490 m. That's how you know (because the constant represents the height from which an object is dropped in either free fall, which this is, or in parabolic motion).