Final answer:
Using the equations of motion for an object under gravity, and the information provided, the time it takes for the bullet to hit the ground after being fired upward from a 3500 ft. cliff with an initial velocity of 400 ft/s is approximately 15 seconds.
Step-by-step explanation:
To find out how long it takes a bullet to hit the ground after being fired upward from a cliff, we need to use the equations of motion under gravity. The problem states that a gun is fired upward from a 3500 ft. cliff with an initial velocity of 400 feet per second. The equation of motion we can use is:
h = v_i * t + (1/2) * g * t^2
where h is the height above ground, v_i is the initial velocity, t is the time, and g is the acceleration due to gravity (32.2 ft/s^2 downward).
However, because the bullet is fired upwards, the initial velocity (v_i) would be -400 ft/s when considering upward as the negative direction. The height (h) when the bullet hits the ground will be -3500 ft. We set up the equation as:
-3500 = -400 * t + (1/2) * 32.2 * t^2
which simplifies to:
0 = 16.1 * t^2 - 400 * t - 3500
This is a quadratic equation of the form at^2 + bt + c = 0, which we can solve for t using the quadratic formula:
t = (-b ± sqrt(b^2 - 4ac)) / (2a)
Plugging in the values, we solve for the positive value of t that gives the time until the bullet hits the ground. Of the given choices, we find that the correct answer is D. 15 seconds.