A flare is launched straight up with a velocity of 200 feet per second. The function h(t)= 200t−16t^2 models the height h(t)of the flare
are at time t. How many seconds will it take for the flare to hit the ground?
just solve for t when h(t) = 0.
To find out how many seconds it will take for the flare to hit the ground, we need to determine when the height of the flare, given by the function h(t), becomes zero.
Given the function h(t) = 200t - 16t^2, we can set it equal to zero:
0 = 200t - 16t^2
Now we can solve this quadratic equation. Rearranging the equation, we get:
16t^2 - 200t = 0
Factoring out common terms, we have:
16t(t - 12.5) = 0
Setting each factor equal to zero, we get:
16t = 0 or t - 12.5 = 0
From the first equation, we can see that t = 0. However, since time cannot be negative in this context, we can ignore this solution.
From the second equation, we find:
t - 12.5 = 0
t = 12.5
Therefore, it will take 12.5 seconds for the flare to hit the ground.
To find out how many seconds it will take for the flare to hit the ground, we need to determine the time when the height of the flare is zero. In other words, we need to find the value of t when h(t) = 0.
Given the function h(t) = 200t - 16t^2, we can set it equal to zero:
0 = 200t - 16t^2
To solve this quadratic equation, we can rearrange it to the standard form:
16t^2 - 200t = 0
Now, we can factor out the common term t:
t(16t - 200) = 0
Setting each factor equal to zero, we get two potential solutions:
t = 0 or 16t - 200 = 0
The first solution t = 0 means that the flare starts at the ground, so it is not the one we're interested in. We need to solve the second equation for t:
16t - 200 = 0
16t = 200
t = 200/16
t = 12.5
Therefore, it will take 12.5 seconds for the flare to hit the ground.