Answer:
Discriminant = 55.2 > 0 -> 2 real solutions
Solutions: t1 = -1.1663 s and t2 = 0.35 s
The solution t1 doesn't make sense for this problem, as we can't have a negative value for the time.
So the solution is t2 = 0.35 s
Step-by-step explanation:
To find the time when the ball will reach the height of 2 meters, we just need to use the value of h = 2 in the equation given. So, we have that:
−4.9t^2 − 4t + 4 = 2
−4.9t^2 − 4t + 2 = 0
For this equation, we have the constants a = -4.9, b = -4 and c = 2. So the discriminant Delta is:
Delta = b^2 - 4ac = 16 + 39.2 = 55.2
sqrt(Delta) = 7.4297
As Delta > 0, we have 2 real solutions
t1 = (-b + sqrt(Delta)) / 2a = (4 + 7.4297) / (-9.8) = -1.1663 s
t2 = (-b - sqrt(Delta)) / 2a = (4 - 7.4297) / (-9.8) = 0.35 s
Number of real solutions: 2
Solutions: t1 = -1.1663 s and t2 = 0.35 s
The solution t1 doesn't make sense for this problem, as we can't have a negative value for the time.
So the solution is t2 = 0.35 s
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