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A policeman fires his gun into the air. The muzzle velocity of his side arm is 300 m/s. How fast is the bullet traveling after 40 seconds, and what direction is the bullet moving?

a) Velocity: 0 m/s, Direction: Downwards
b) Velocity: 300 m/s, Direction: Upwards
c) Velocity: 300 m/s, Direction: Downwards
d) Velocity: 0 m/s, Direction: Upwards

1 Answer

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Final answer:

The bullet will have stopped ascending and will be falling downwards after 40 seconds. Therefore, it will be moving downwards, but the velocity will not be 300 m/s, it'll be moving at terminal velocity as it would have already reached its peak and started falling.

Step-by-step explanation:

The question involves projectile motion and the effects of gravity in physics. When a bullet is fired into the air, it is initially traveling at the muzzle velocity, which in this case is 300 m/s upwards. As the bullet ascends, it's slowed down by gravity, which has an acceleration of approximately 9.81 m/s² downwards. After a certain time, gravity will bring the bullet to a complete stop momentarily before it begins to fall back to Earth.

To find out how fast the bullet is moving after 40 seconds, we use the formula for velocity affected by acceleration (gravity):

final velocity = initial velocity - (acceleration * time)

v = 300 m/s - (9.81 m/s² * 40 s) = 300 m/s - 392.4 m/s

Since the result is a negative number, it implies that after 40 seconds, the bullet has not only stopped but also started to descend. This time duration is much greater than what it would take for the bullet to reach its maximum height and begin falling back. Therefore, the correct answer would be that after 40 seconds, the bullet is traveling small or at terminal velocity downwards.

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