Final answer:
Using kinematic equations, none of the provided options correctly represent the maximum height or the time in the air for a bullet fired straight upwards at 1000 m/s without air resistance. Instead, the bullet would reach approximately 51020 meters with a total time in air of about 204 seconds.
Step-by-step explanation:
To determine the maximum height a bullet would reach if fired straight upwards at 1000 m/s without air resistance, we utilize the kinematic equation for displacement in vertical motion which is h = (v^2) / (2g), where h is the maximum height, v is the initial velocity, and g is the acceleration due to gravity (9.81 m/s^2). Plugging in the values, we get h = (1000 m/s)^2 / (2 * 9.81 m/s^2), which calculates to approximately 51020 meters or 51 kilometers.
Regarding the time in the air, we use the time of ascent equation t = v / g, which gives us t = 1000 m/s / 9.81 m/s^2 that results in approximately 102 seconds to reach the maximum height. However, since the bullet takes the same amount of time to descend, we must double this to find the total time in the air, leading to about 204 seconds.
Thus, none of the provided options (a, b, c, d) correctly represents the bullet's maximum height or the time in the air under the given scenario.