A bullet fired from a gun vertically upward with a muzzle velocity of 500 m/s. A) How long is the highest point reached? B) How long does it take the bullet to reach the ground after it is fired?
A. V = Vo + g*t = 0
500 - 9.8t = 0
9.8t = 500
Tr = 51.02 s. = Rise time = Time to reach max ht.
B. T = Tr+Tf
Tf = Tr = 51.02 s. = Fall time.
T = 51.02 + 51.02 = 102.04 s. to reach
gnd.
To find the answer to these questions, we need to understand the motion of the bullet in two phases: upward motion and downward motion.
A) To determine the time taken to reach the highest point of its trajectory, we can use the following formula:
Time taken to reach highest point (t_max) = (Final velocity - Initial velocity) / Acceleration
In this case, the final velocity at the highest point is 0 m/s (as the bullet momentarily stops before falling back down). The initial velocity is given as 500 m/s, and the acceleration is equal to the acceleration due to gravity, which is approximately 9.8 m/s^2 (assuming no air resistance).
Substituting these values into the equation, we have:
t_max = (0 - 500) / (-9.8)
= -500 / (-9.8)
≈ 51 seconds
Therefore, it takes approximately 51 seconds for the bullet to reach the highest point of its trajectory.
B) To determine the total time taken for the bullet to reach the ground after it is fired, we can consider the entire journey, including the upward and downward motion. The time for the downward motion will be the same as the time taken for the upward motion (t_max), as the bullet falls back down symmetrically.
Thus, the total time taken for the bullet to reach the ground after it is fired can be calculated as:
Total time = 2 * t_max
= 2 * 51
= 102 seconds
Therefore, it takes approximately 102 seconds for the bullet to reach the ground after it is fired.