Answer:
The reasonable domain for the scenario is option 'a';
a) [0, 7]
Explanation:
For the projectile motion of the object, we are given;
The speed at which the object is launched, v = 29.4 meters per second
The height of the platform from which the object is launched, h = 34.3 meter
The equation for the height of the object as a function of time 'x' is given as follows;
f(x) = -4.9·x² + 29.4·x + 34.3
The domain for the scenario, is given by the possible values of 'x' for the function, which is found as follows;
At the height from which the object is launched, x = 0, and f(x) = 34.3
At the ground level to which the object can drop, f(x) = 0
∴ f(x) = -4.9·x² + 29.4·x + 34.3 = 0
-4.9·x² + 29.4·x + 34.3 = 0
By the quadratic formula, we have;
x = (-29.4 ± √(29.4² - 4 × (-4.9) × 34.3))/(2 × (-4.9)
∴ x = -1, or 7
Given that time is a natural number, we have the reasonable domain for the scenario as the start time when the object is launched, t = 0 to the time the object reaches the ground, t = 7
Therefore, the reasonable domain for the scenario is; 0 ≤ x ≤ 7 or [0, 7].