Please explain the answers. Thank You
1. A rifle is fired horizontally over a large flat plane. At the instant the rifle is fired, a student drops a second identical bullet from the
same height as the rifle. Which bullet hits the ground first?
2. A monkey is hanging from a tree branch. A scientist wants to shoot the monkey with a tranquilizer dart so she can study the monkey. She knows the monkey will be startled by the sound of the tranquilizer gun and will let go of the branch at the instant the gun is
fired. Where should the scientist aim to hit the monkey? (Above it, below it or directly at it?)
1. D1 = Vx * Tf
h = 0.5g*Tf^2
Tf^2 = h/0.5g
Tf = sqrt (h/0.5g) = Fall time of fired
bullet.
h = 0.5g*Tf^2
Tf^2 = h/0.5g
Tf = sqrt (h/0.5g) = Fall time of the
dropped bullet.
Therefore, the fall times are equal.
2. Directly at it.
1. In order to determine which bullet hits the ground first, we need to understand the concept of horizontal motion and vertical motion. When a rifle is fired horizontally, the bullet is given an initial horizontal velocity but no vertical velocity. This means that the bullet will continue moving horizontally at a constant speed until it hits the ground. On the other hand, when the student drops the second bullet, it has an initial vertical velocity due to gravity but no horizontal velocity. This means that the bullet will only be affected by the force of gravity and will accelerate vertically downward.
Since both bullets are starting at the same height, the bullet fired from the rifle will take longer to reach the ground because it is covering both horizontal and vertical distances. In the time it takes for the fired bullet to reach the ground, the dropped bullet will have fallen vertically downward and will hit the ground first.
Therefore, the second bullet dropped by the student hits the ground first.
2. To determine where the scientist should aim in order to hit the monkey, we need to consider the monkey's motion when it lets go of the branch. When the monkey lets go of the branch, it will start falling vertically downward due to gravity. However, it will also continue to have some horizontal momentum from its initial position on the branch.
In order to hit the monkey, the scientist needs to take into account both the vertical and horizontal motion of the monkey. Since the monkey is falling, the scientist should aim above the monkey to compensate for the time it takes for the tranquilizer dart to reach the monkey's position. By aiming directly at the monkey, the dart would only reach the position where the monkey was when the gun was fired, not accounting for the monkey's vertical motion.
Therefore, the scientist should aim above the monkey in order to hit it.