A clown was shot out of a cannon at ground level. Her height above the ground at any time (t) was given by the function h(t) = -15t2 + 15t
What was height at t(1), t(2),and t(3)?
The flight will last how many seconds??
figure h when t=1, 2, and 3
the flight finished when h(t)=0
solve for t.
To find the height at a specific time t, you can substitute the value of t into the function h(t) = -15t^2 + 15t.
1. For t(1):
Plug in t = 1 into the function:
h(1) = -15(1)^2 + 15(1)
= -15 + 15
= 0
Therefore, the height at t(1) is 0.
2. For t(2):
Plug in t = 2 into the function:
h(2) = -15(2)^2 + 15(2)
= -15(4) + 30
= -60 + 30
= -30
Therefore, the height at t(2) is -30.
3. For t(3):
Plug in t = 3 into the function:
h(3) = -15(3)^2 + 15(3)
= -15(9) + 45
= -135 + 45
= -90
Therefore, the height at t(3) is -90.
To calculate the duration of the flight, we need to find when the clown lands, i.e., the time when the height is 0.
Set h(t) = 0:
0 = -15t^2 + 15t
Factor out 15t:
0 = 15t(-t + 1)
This equation is satisfied when t = 0 or t = 1. Since t = 0 represents the initial height (ground level), we can discard this solution.
Therefore, the flight will last 1 second since the clown lands at t = 1.