okay so the equation is -4.9t^2 - 39.2t + 1.6
If the rockets explode at the highest point (which max height is 80 meters) One of the rockets is schedules to explode 2 minutes and 28 seconds into the program. When should the rocket be fired from the barge? (How long, from start of the program, before the rocket is fired)
plllllleaaassse hellp! thanks so much and godbless
4 minutes ago - 4 days left to answer.
Additional Details
so t is height of an object
and this equation = H(t)
31 seconds ago
To find when the rocket should be fired from the barge, we need to determine the time it takes for the rocket to reach its highest point. We know that the maximum height is 80 meters.
Step 1: Set up the equation
We can use the equation -4.9t^2 - 39.2t + 1.6 = 80, where t represents the time in seconds.
Step 2: Solve the equation for t
Rewriting the equation, we have -4.9t^2 - 39.2t + 1.6 - 80 = 0.
Simplifying further, we get -4.9t^2 - 39.2t - 78.4 = 0.
Step 3: Use the quadratic formula
To solve for t, we can use the quadratic formula: t = (-b ± √(b^2 - 4ac)) / (2a).
In this case, a = -4.9, b = -39.2, and c = -78.4.
Step 4: Calculate t
Plugging in the values to the quadratic formula, we get:
t = (-(-39.2) ± √((-39.2)^2 - 4(-4.9)(-78.4))) / (2(-4.9))
Simplifying further:
t = (39.2 ± √(1536.64 - 1530.56)) / (-9.8)
t = (39.2 ± √6.08) / (-9.8)
Now, we have two possible values for t: t1 and t2.
t1 = (39.2 + √6.08) / (-9.8)
t2 = (39.2 - √6.08) / (-9.8)
Step 5: Choose the appropriate value of t
Since we are interested in when the rocket should be fired from the barge, we should consider the positive value of t that represents the time before the rocket is fired. Therefore, we choose t1.
Step 6: Convert the time into minutes and seconds
We need to convert t1 into minutes and seconds. Since each minute has 60 seconds, we'll divide t1 by 60 to get the minutes and take the remainder as the seconds.
t1 = (39.2 + √6.08) / (-9.8)
t1 ≈ 1.77 seconds
Converting seconds to minutes and seconds:
1.77 seconds ≈ 1 minute 46 seconds
Therefore, the rocket should be fired from the barge approximately 1 minute and 46 seconds into the program.
To find the time at which the rocket should be fired from the barge, we need to find the time when the rocket reaches a height of 80 meters.
We can set up the equation H(t) = 80 and solve for t.
The given equation is: -4.9t^2 - 39.2t + 1.6 = 80
To solve this quadratic equation, we can rearrange it to standard form: -4.9t^2 - 39.2t + 1.6 - 80 = 0
Simplifying, we have: -4.9t^2 - 39.2t - 78.4 = 0
Now, we can use the quadratic formula: t = (-b ± √(b^2 - 4ac)) / 2a
For this equation, a = -4.9, b = -39.2, and c = -78.4
Plugging in these values, we get: t = (-(-39.2) ± √((-39.2)^2 - 4(-4.9)(-78.4))) / (2(-4.9))
Simplifying further, we have: t = (39.2 ± √(1536.64 - 1524.64)) / (-9.8)
Calculating the square root and simplifying, we get: t = (39.2 ± √12) / (-9.8)
Now, we can find the two possible values of t:
t1 = (39.2 + √12) / (-9.8) ≈ -2.305 seconds
t2 = (39.2 - √12) / (-9.8) ≈ 0.858 seconds
Since time cannot be negative in this context, we discard t1 and consider t2.
Therefore, the rocket should be fired approximately 0.858 seconds (or about 0.86 seconds) before the program starts.