Complete question is:An orange is shot up into the air with a catapult. The function h given by h(t) = 15 + 60t - 16t² models the orange’s height, in feet, t seconds after it was launched.
Select all the true statements about the situation.
Options:
1. The domain of function h only contains values greater than or equal to 0.
2. The orange is at the same height 1 second after launch and 2 seconds after launch.
3. After 3 seconds, the orange has hit the ground.
4. The orange is 15 feet above the ground when it is launched.
5. The value t = 10 does not belong to the domain of h.
Answer:
Option 1 - True
Option 2 - False
Option 3 - False
Option 4 - True
Option 5 - True
Step-by-step explanation:
Looking at the options,
-The domain is the x or t value and it is time. Now, time can only be positive or greater than or equal to zero i.e. t ≥ 0. Thus, option 1 is true.
- At t = 1 second;
h = 15 + 60(1) - 16(1)²
h = 15 + 60 - 16 = 59 ft
Also, at t = 2 seconds;
h = 15 + 60(2) - 16(2)²
h = 15 + 120 - 64 = 71 ft
So,value of h is not the same at t = 1 and t = 2. Thus, option 2 is not true.
- The orange will hit the ground when h(t) = 0.
However, at t = 3;
h(t) = 15 + 60(3) - 16(3)²
h(t) = 51 ft
h(t) is not equal to zero at t = 3, so option 3 is false
- when the orange is launched it is at time t = 0.
Thus,
h(0) = 15 + 60(0) - 16(0)²
h(0) = 15 ft
So option 4 is true.
- At t=10, h(t) = 15 + 60(10) - 16(10)²
h(10) = -985
This means the orange would be below ground level and thus doesn't belong to the domain of h, so option 5 is true.
