Physics 101 mechanics help -- Bullet fired by a rifle barrel

In summary, the acceleration of the bullet in the barrel is 2.8*10^5m/s^2, and the position of the bullet is initially at zero when t=0. The length of time the bullet is accelerated is unknown and the speed at which it leaves the barrel is also unknown. The length of the barrel is also unknown. The relevant equation is v = (−5.00 ✕ 10^7)t^2 + (2.80 ✕ 10^5)t. The derivative of this equation is a= dv/dt = 2(5*10^5)t+2.8*10^5. The coefficient should be -5*10^7 instead of +5
  • #1
EishaR
1
0
Homework Statement
A repeating rifle fires 2 LR bullets such that as they travel down the barrel of the rifle their speed is given by v = (−5.00 ✕ 107)t2 + (2.80 ✕ 105)t,where v is in meters per second and t is in seconds. The acceleration of the bullet just as it leaves the barrel is zero.
Determine the acceleration (in m/s2) and position (in m) of the bullet as a function of time when the bullet is in the barrel. (Use the following as necessary: t. Round all numerical coefficients to at least three significant figures. Do not include units in your answers. Assume that the position of the bullet at t = 0 is zero.)
a (t)=
x(t)=

(b)Determine the length of time the bullet is accelerated (in s).

(c) Find the speed at which the bullet leaves the barrel (in m/s).

(d) What is the length of the barrel (in m)?
Relevant Equations
y v = (−5.00 ✕ 10^7)t2 + (2.80 ✕ 10^5)t,
a) a= dv/dt = 2(5*10^5)t+2.8*10^5
2(5*10^5)(0)+2.8*10^5=2.8*10^5m/s^2
 
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  • #2
EishaR said:
Homework Statement:: A repeating rifle fires 2 LR bullets such that as they travel down the barrel of the rifle their speed is given by v = (−5.00 ✕ 107)t2 + (2.80 ✕ 105)t,where v is in meters per second and t is in seconds. The acceleration of the bullet just as it leaves the barrel is zero.
Determine the acceleration (in m/s2) and position (in m) of the bullet as a function of time when the bullet is in the barrel. (Use the following as necessary: t. Round all numerical coefficients to at least three significant figures. Do not include units in your answers. Assume that the position of the bullet at t = 0 is zero.)
a (t)=
x(t)=

(b)Determine the length of time the bullet is accelerated (in s).

(c) Find the speed at which the bullet leaves the barrel (in m/s).

(d) What is the length of the barrel (in m)?
Relevant Equations:: y v = (−5.00 ✕ 10^7)t2 + (2.80 ✕ 10^5)t,

a) a= dv/dt = 2(5*10^5)t+2.8*10^5
2(5*10^5)(0)+2.8*10^5=2.8*10^5m/s^2
For the first part, check your derivative. You must attempt the other parts also.
 
Last edited:
  • #3
How did −5.00 ✕ 10^7 turn into +5.00 ✕ 10^5?
 

1. How does the velocity of a bullet fired by a rifle barrel affect its trajectory?

The velocity of a bullet fired by a rifle barrel is a crucial factor in determining its trajectory. The higher the velocity, the farther the bullet will travel and the flatter its trajectory will be. This is due to the fact that a higher velocity means the bullet is moving faster and therefore has less time to be affected by external forces such as gravity and air resistance.

2. What is the role of gravity in the flight of a bullet?

Gravity is a major force that affects the flight of a bullet fired by a rifle barrel. As the bullet travels through the air, it is constantly pulled towards the ground by gravity. This causes the bullet to follow a curved path, known as a parabola, until it reaches the ground. The angle at which the bullet is fired also plays a role in how gravity affects its flight.

3. How does air resistance impact a bullet's trajectory?

Air resistance, also known as drag, is another important factor in the flight of a bullet fired by a rifle barrel. As the bullet moves through the air, it encounters resistance from the air molecules around it. This resistance can slow down the bullet and cause it to drop more quickly, resulting in a shorter flight distance and a steeper trajectory. The shape and velocity of the bullet can also affect the amount of air resistance it experiences.

4. What is the relationship between the mass of a bullet and its velocity?

The mass of a bullet and its velocity have an inverse relationship. This means that as the mass of the bullet increases, its velocity decreases and vice versa. This is due to the principle of conservation of momentum, which states that the total momentum of a system remains constant. Therefore, a heavier bullet will have a lower velocity compared to a lighter bullet when fired from the same rifle barrel.

5. How does the angle at which a bullet is fired affect its trajectory?

The angle at which a bullet is fired from a rifle barrel can greatly impact its trajectory. A bullet fired at a higher angle will have a longer flight distance and a flatter trajectory compared to a bullet fired at a lower angle. This is because a higher angle allows the bullet to travel a longer horizontal distance before being pulled down by gravity, resulting in a longer flight path.

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