Question

A rifle bullet is shot vertically upward. Twenty-three seconds later the bullet has a velocity of 72.0 m/s, downward. What is the velocity of the bullet when the bullet leaves the rifle?

Answer 1

Using the principles of kinematics, the bullet's initial velocity when it leaves the rifle is determined to be 112.815 m/s upwards, calculated by knowing that the bullet takes an equal amount of time to ascend and descend in its 23-second journey.

Step-by-step explanation:

To determine the initial velocity of the bullet when it leaves the rifle, we need to use the principles of kinematics under the influence of gravity. Given that the bullet is shot vertically upward and comes back down with a velocity of 72.0 m/s after 23 seconds, we can use the equation of motion:

v = u + at

Where v is the final velocity, u is the initial velocity, a is the acceleration (which is due to gravity and hence -9.81 m/s²), and t is the time.

We recognize that the bullet's upward journey and downward journey take equal time. Hence, the bullet takes 11.5 seconds to reach the top and another 11.5 seconds to come back down. We can now solve for the initial velocity.

Setting the final velocity at the highest point to 0 (as it momentarily stops before coming down), we have:

0 = u - (9.81 m/s² * 11.5 s)

Solving for u, we get:

u = 9.81 m/s² * 11.5 s

= 112.815 m/s

Therefore, the initial muzzle velocity of the bullet is 112.815 m/s upwards.