Question

An orange is shot up into the air with a catapult. The function given by h(t)+20+60t-16t² models the oranges height in feet, t seconds after it was launched.
Select all true statements
A. The domain of function a includes negative values
B. The orange is at the same height 1 second after launch and 2 seconds after launch
C the orange hits the ground a little after 4 seconds
D the Value t=10 is part of the domain of h
E. The orange is 20 feet above the ground when it is launched

Answer 1

Answer:

  C, E

Step-by-step explanation:

As a rule, these ballistic motion equations are only applicable for heights above the final resting place. Usually, that is the ground (h=0). Time is always measured as a non-negative quantity beginning at the time of launch.

The function is meaningless after the time the object comes to rest on the ground, so the domain of the function extends from 0 until that time.

These considerations allow us to evaluate the offered statements.

  A. The domain never includes negative values. (A is not a true statement)

  B. The heights are the same at times that are symmetrical around the time of the maximum height. Here, that time is about 1.9 seconds, not 1.5 seconds, so the heights will be different at 1 and 2 seconds after launch. (B is not a true statement)

  C. The graph of the function shows the height reaches 0 at about 4.06 seconds, a little after 4 seconds. (C is true)

  D. Based on our answer to C, we know t=10 is outside the domain of the function. (D is not a true statement)

  E. The value of the function is 20 when t=0, so the function tells us the orange is 20 feet above the ground when it is launched. (E is true)

The true statements are C and E.