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?

when v = 0, we are at the top

v = Vi - g t
0 = 500 - 9.81 t
solve for t

multiply t by 2 to get total time (parabola up to vertex and back down, symmetry)

To calculate the time taken for the bullet to reach the highest point (A), we need to use a specific formula. Given that the initial velocity (u) is 500 m/s, the final velocity (v) at the highest point is 0 m/s (since the bullet momentarily stops), and the acceleration (a) due to gravity is approximately -9.8 m/s² (negative because it acts in the opposite direction of motion), we can use the formula:

v = u + at

Rearranging the formula to solve for time (t):

t = (v - u) / a

Substituting the given values:

t = (0 - 500) / -9.8
t ≈ 51 seconds (rounded to the nearest second)

Therefore, it takes around 51 seconds for the bullet to reach the highest point.

To calculate the time taken for the bullet to reach the ground after it is fired (B), we need to consider the entire trajectory of the bullet. The bullet is fired vertically upward and then falls back down due to gravity. The total time of flight can be determined by finding the time taken to reach the highest point and doubling it.

Thus, the time taken for the bullet to reach the ground after it is fired is approximately 2 * 51 = 102 seconds (rounded to the nearest second).