Three marksmen stand at the top of a building. Two of them fire identical bullets out of identical rifles. The bullets leave the rifles with the same initial speed. The last marksman forgot his rifle, so he drops his bullet off the edge of the building from the same height as the other bullets are fired. Assume that air resistance can be ignored. Select the bullet or bullets that will hit the ground first.
a.) The bullet that is fired horizontally
b.) The bullet that is fired at an angle of 30° above the horizontal
c.) The bullet that is dropped
To determine which bullet will hit the ground first, we need to consider the horizontal and vertical components of motion for each bullet.
a.) The bullet that is fired horizontally:
When a bullet is fired horizontally, its initial velocity in the vertical direction is zero. However, it still has an initial velocity in the horizontal direction. As a result, there is no vertical acceleration acting on the bullet, but there is horizontal acceleration due to gravity. Since the bullet only experiences the horizontal acceleration, it will take the same amount of time to reach the ground as a bullet dropped vertically. Therefore, it will hit the ground at the same time as the dropped bullet.
b.) The bullet that is fired at an angle of 30° above the horizontal:
When a bullet is fired at an angle above the horizontal, it has both horizontal and vertical components of velocity. The vertical component is affected by gravity and experiences an acceleration of -9.8 m/s^2 (assuming no air resistance). The horizontal component, however, is not affected by gravity and remains constant throughout the motion. Since the bullet is fired with the same initial speed as the horizontally fired bullet, but at an angle, it will have a shorter time of flight compared to the horizontal bullet. Therefore, it will hit the ground before the horizontally fired bullet.
c.) The bullet that is dropped:
The bullet that is dropped vertically experiences only the vertical component of gravity, which is an acceleration of -9.8 m/s^2 (assuming no air resistance). Since it starts from rest vertically and falls straight down, it will hit the ground after falling for a certain amount of time. This time of flight will be longer than the time it takes for the bullet fired at an angle above the horizontal to hit the ground.
Therefore, in this scenario, the correct answer is:
b.) The bullet that is fired at an angle of 30° above the horizontal