A bullet is dropped into a river from a very high bridge. At the same time, another bullet is fired from a gun straight down towards the water. If air resistance is negligible, how do the accelerations of the bullets compare just before they strike the water?
the accelerations are the same
the velocities are different
The acceleration of an object is due to the force acting on it. Assuming that gravity is the only force acting on the bullets, their accelerations will be the same just before they strike the water.
In the case of the dropped bullet, it is initially at rest and then accelerates downward under the influence of gravity. The acceleration due to gravity is approximately 9.8 m/s^2, directed downward.
For the bullet fired from the gun, it is also subject to the force of gravity and accelerates downward at the same rate. The initial velocity due to the firing of the gun does not affect the acceleration because it acts horizontally and does not contribute to the downward acceleration.
Therefore, just before striking the water, both bullets will have the same acceleration of approximately 9.8 m/s^2, directed downward.
To compare the accelerations of the two falling bullets just before they strike the water, we first need to understand the forces acting on each bullet.
1. Bullet dropped into the river:
When the bullet is dropped into the river, it only experiences the force of gravity pulling it downwards. The acceleration of a freely falling object due to gravity is approximately 9.8 m/s^2, directed downward.
2. Bullet fired from the gun:
When the bullet is fired from the gun, it experiences the force of gravity pulling it downwards and the force of air resistance opposing its motion. However, in this case, air resistance is assumed to be negligible, meaning that it can be ignored. Therefore, the only force acting on the bullet fired from the gun is gravity.
Since both bullets are only affected by gravity (and neglecting air resistance), they will experience the same acceleration just before they strike the water. This acceleration is approximately 9.8 m/s^2, directed downward.
Therefore, the accelerations of the two bullets are comparable and equal just before they hit the water.