Final answer:
The maximum height of an arrow fired at an initial velocity of 160 feet per second can be calculated using the kinematic equation for projectile motion. With an initial upward velocity and the acceleration due to gravity, the maximum height is found to be 400 feet, which is not listed in the given options.
Step-by-step explanation:
The question regarding the arrow fired into the air involves calculating the maximum height, which can be solved using kinematic equations under the physics of projectile motion. By knowing the initial velocity and the acceleration due to gravity (32 feet per second squared, downward), we can find the maximum height that the arrow will reach. For an initial velocity (v0) of 160 feet per second vertically upwards and considering the acceleration due to gravity (g = -32 ft/s2), the time (t) to reach the maximum height is found when the final velocity (v) at the peak is zero.
Using the equation v = v0 + gt, we have 0 = 160 - 32t, which gives us t = 160/32 = 5 seconds. Now, we calculate the maximum height (h) using the equation h = v0t + (1/2)gt2. Plugging in the values, we get h = 160 * 5 - 0.5 * 32 * 52, which results in a maximum height of 400 feet.
However, none of the given answer options (A, B, C, D) match this calculated height. Therefore, the information provided in the choices might be incomplete or incorrect. The correct maximum height based on the provided initial velocity and the physics of projectile motion is 400 feet, which is not represented in the given options.