Two flares are launched from a life raft. The height h of the first flare in metres above the sea is modelled by the formula h1= t2+t+1meters,and the second flare is h2=4-t where t is the time
12 in seconds after the flare is launched. Determine
(i) Time taken and
(ii) Height when the two flares meet each other.
Hint: When two flares meet each other, their heights are the same (h1=h2).
Vinny, I count 6 consecutive posts by you of rather diverse problems, some requiring knowledge of physics.
I did the first one for you.
You have shown no work or indication that you have tried these, and it looks like just a "homework dump". Where do your difficulties arise ?
To find the time taken and the height when the two flares meet each other, we need to set their heights equal to each other and solve for both variables.
(i) Time taken:
To find the time taken, we set h1 equal to h2 and solve for t:
h1 = h2
t^2 + t + 1 = 4 - t
Rearranging the equation:
t^2 + t + t + 1 - 4 = 0
t^2 + 2t - 3 = 0
We now have a quadratic equation. We can solve this equation by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values into the formula:
t = (-2 ± √(2^2 - 4(1)(-3))) / (2(1))
t = (-2 ± √(4 + 12)) / 2
t = (-2 ± √16) / 2
t = (-2 ± 4) / 2
We get two solutions for t: t = 1 and t = -3. However, since time cannot be negative, we discard t = -3. Therefore, the time taken for the two flares to meet is t = 1 second.
(ii) Height when the two flares meet:
To find the height when the two flares meet, we substitute the value of t = 1 into either h1 or h2. Let's substitute it into h1:
h1 = t^2 + t + 1
Plugging in t = 1:
h1 = 1^2 + 1 + 1
h1 = 1 + 1 + 1
h1 = 3
So, when the two flares meet each other, their height is 3 meters above the sea.