(1) A ball is thrown vertically upward from a 25 foot platform the function is s(t) = -16t^2 + 11t + 25, when will the object fall back to the ground after, choose the correct answer a) 1.64 b) -1.64 c) 0.95 d) -0.95;
(2) seconds because ______ (choose the correct answer) a) 1.64 b) 0.95 c) -1.64 d) -0.95 cannot be a solution
To find when the object will fall back to the ground, we need to find the time at which the height, represented by the function s(t), is equal to 0.
Given the function s(t) = -16t^2 + 11t + 25, we set it equal to 0:
-16t^2 + 11t + 25 = 0
To solve this quadratic equation, we can use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a = -16, b = 11, and c = 25.
Substituting the values into the quadratic formula:
t = (-11 ± √(11^2 - 4(-16)(25))) / (2(-16))
Simplifying this equation further:
t = (-11 ± √(121 + 1600)) / (-32)
t = (-11 ± √(1721)) / (-32)
Since the object is thrown vertically upward, we can discard the negative solution (-1.64) as it represents the time before the ball was thrown. Therefore, the correct answer is (1) a) 1.64.
The answer to (2) is a) 1.64 because the time taken for the object to fall back to the ground is a positive quantity. Negative solutions, such as -1.64, do not make sense in this context as time cannot be negative.