An archer aims an arrow precisely horizontally over a large, flat field and lets it fly. At the same instant, the archer's watchband breaks and the watch falls to the ground. Does the watch hit the ground before, at the same times as, or after the arrow hits the ground? Defend your answer
Same time. Same distance to drop. Mass does not effect the result. Both start from the same height at the same time, with no initial downward component.
To determine whether the watch hits the ground before, at the same time as, or after the arrow, we need to consider the factors affecting the motion of both objects.
Since the arrow is shot precisely horizontally, we can assume that it has an initial horizontal velocity component and no vertical velocity component. The only force acting on the arrow is gravity, which will cause it to fall down due to acceleration. Without any initial vertical velocity, the arrow will follow a parabolic trajectory.
On the other hand, the watch falls vertically from the archer's wrist without any initial horizontal velocity. The only force acting on the watch is gravity, causing it to accelerate downward. Since there is no horizontal motion involved, its trajectory will be vertical.
Both the arrow and the watch experience the same acceleration due to gravity, which is approximately 9.8 m/s² near the Earth's surface. However, their initial velocities and trajectories are different.
If we neglect air resistance, which is a reasonable assumption for this scenario, the time of flight for both the arrow and the falling watch will depend solely on their initial vertical positions. As the arrow is already at some distance from the ground horizontally, it will take longer to reach the ground compared to the watch. Therefore, the arrow will hit the ground after the watch.
In conclusion, the watch will hit the ground before the arrow does.
The watch and the arrow would hit the ground at the same time, assuming there are no external factors affecting the motion of either object. This can be explained using the principles of projectile motion.
When the archer shoots the arrow horizontally, it will follow a parabolic trajectory. The only force acting on the arrow horizontally is the initial velocity imparted by the archer. However, in the vertical direction, the arrow is subject to the force of gravity, which causes it to accelerate downward.
On the other hand, when the watch falls, it is only subject to the force of gravity.
Since both objects are subject to the same acceleration due to gravity, they would fall at the same rate. This means that regardless of their initial horizontal velocities, they would both cover the same vertical distance in the same amount of time. Consequently, the watch and the arrow would hit the ground at the same time.
It is important to note that this scenario assumes there are no factors such as air resistance or wind that could affect the motion of the two objects differently.