# Bow and arrows, Newtons second law of physics

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In summary, the question is whether an arrow's speed would slow down due to air resistance and if that means the acceleration would be de-accelerating. The equation f=ma is mentioned, but the conversation is not a homework problem. The speaker suggests that in an environment with no air or gravity, the arrow's velocity would increase due to no change in acceleration. However, in reality, the arrow would decelerate due to air resistance. The speaker also mentions a differential equation to explain the arrow's decreasing speed.
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## Homework Statement

If I have shot an arrow, would that arrow speed slow down due to air resistance? If so, would that mean that the the acceleration would be de-accelerating?

f = ma

## The Attempt at a Solution

This isn't a a homework problem, this is just something I was wondering about the basic laws

Any who, If I shot an arrow where there is air but no gravity, would the arrow eventually slow down? Because i'd imagine if there was no air than the velocity/speed would increase because the acceleration wouldn't change.

Please elaborate fully, this is my first time taking physics, I just want to learn.

Once you've shot the arrow, you are no-longer applying some force on it, but the air does ! It's only decelerating by the air resistance, assuming you know calculus
F(air resistance) = -λ(some coefficient)*v(velocity) and you end up with a differential equation whose solution is v(t) = V0 * e(-λt) , speed is falling but at least he have one :)

## 1. How does Newton's second law of physics apply to bow and arrows?

According to Newton's second law, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. In the case of bow and arrows, the force applied to the arrow by the string is what determines its acceleration, while the mass of the arrow affects how quickly it will travel.

## 2. What is the relationship between force and acceleration in the context of bow and arrows?

The greater the force applied to the arrow by the string, the greater the acceleration of the arrow. This means that a stronger pull on the string will result in a faster and more powerful shot.

## 3. How does the mass of the arrow affect its speed when shot from a bow?

In general, a lighter arrow will travel faster than a heavier one when shot from the same bow. This is because the lighter arrow will experience a greater acceleration due to the same amount of force applied by the string.

## 4. Can you explain the concept of inertia in relation to bow and arrows?

Inertia refers to an object's tendency to resist changes in its state of motion. In the context of bow and arrows, inertia can be seen when an arrow is released from the bow. The force of the string pushes the arrow forward, but its inertia causes it to continue moving in a straight line until acted upon by an external force, such as air resistance.

## 5. How does the angle of the bow affect the trajectory of the arrow?

The angle of the bow, or the degree to which it is drawn back, can greatly affect the trajectory of the arrow. A shallower angle will result in a shorter and lower shot, while a steeper angle will result in a longer and higher shot. This is because the steeper angle allows for more force to be applied to the arrow, resulting in a greater acceleration and thus a longer and higher shot.

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