The height of a flare fired can be described as, h=-16t + 60t
T is time and H is height in feet. How long will it take to reach 36 feet
typo
h = -16^2 + 60 t !!!! on earth
happens twice, on the way up and on the way down
36 = -16 t^2 + 60 t
16 t^2 -60 t + 36 = 0
4 t^2 - 15 t + 9 = 0
(4 t - 3)( t - 3) = 0
t = 3/4 on the way up
t = 3 on the way down (but burnt out)
To find out how long it will take for the flare to reach 36 feet in height, we can use the given equation h = -16t^2 + 60t, where h represents the height and t represents the time.
We want to find the value of t when h is equal to 36. So, we can plug in h = 36 into the equation:
36 = -16t^2 + 60t
Now, we can rearrange the equation to form a quadratic equation:
-16t^2 + 60t - 36 = 0
To solve this quadratic equation, we can either factor it or apply the quadratic formula. However, in this case, factoring might not be straightforward, so let's use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
In our equation, a = -16, b = 60, and c = -36. Plugging these values into the formula, we get:
t = (-60 ± √(60^2 - 4 * -16 * -36)) / (2 * -16)
Simplifying further:
t = (-60 ± √(3600 - 2304)) / (-32)
t = (-60 ± √(1296)) / (-32)
t = (-60 ± 36) / (-32)
Now we have two possible values for t:
t1 = (-60 + 36) / (-32) = -24 / -32 = 0.75
t2 = (-60 - 36) / (-32) = -96 / -32 = 3
Since time cannot be negative, we discard the negative value and consider t = 0.75 as the valid solution.
Therefore, it will take approximately 0.75 seconds for the flare to reach a height of 36 feet.
To find the time it takes for the flare to reach a height of 36 feet, we can substitute the value of H (36 feet) into the equation for height.
h = -16t^2 + 60t
Since we want to find the time it takes to reach 36 feet, we can set h equal to 36 and solve for t:
36 = -16t^2 + 60t
Rearranging the equation to form a quadratic equation:
-16t^2 + 60t - 36 = 0
Now, we can solve this quadratic equation to find the value(s) of t.
We can either factorize the quadratic equation, complete the square, or use the quadratic formula. In this case, let's use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values from our quadratic equation:
t = (-(60) ± √((60)^2 - 4(-16)(-36))) / (2(-16))
Simplifying the equation further:
t = (-60 ± √(3600 - 2304)) / (-32)
t = (-60 ± √(1296)) / (-32)
Taking the square root of 1296:
t = (-60 ± 36) / (-32)
Now, we have two possible solutions:
t1 = (-60 + 36) / (-32) = -24 / (-32) = 0.75
t2 = (-60 - 36) / (-32) = -96 / (-32) = 3
Therefore, the flare will reach a height of 36 feet at two different times: 0.75 seconds and 3 seconds.