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A bullet travelling with a velocity of 16m/s penetrates a tree trunk and come to rest in 0.4m.find the time taken during the retardation?
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A bullet travelling with a velocity of 16m/s penetrates a tree trunk a...
Calculation of Time Taken during Retardation of Bullet


Given Data:


  • Initial velocity of the bullet, u = 16 m/s

  • Distance travelled by the bullet while stopping, s = 0.4 m

  • Final velocity of the bullet, v = 0 m/s (bullet comes to rest)



Formula:

The formula to calculate the time taken during retardation of the bullet is:

v = u + at

Where,

  • u = initial velocity of the bullet

  • v = final velocity of the bullet

  • a = acceleration of the bullet

  • t = time taken by the bullet to come to rest



We know that the bullet comes to rest after covering a distance of 0.4 m. Hence, we can use the equation of motion to calculate the acceleration of the bullet.

Equation of Motion:

The equation of motion for a body under retardation is:

v^2 = u^2 - 2as

Where,

  • u = initial velocity of the bullet

  • v = final velocity of the bullet

  • a = acceleration of the bullet

  • s = distance travelled by the bullet



Calculation:

Substituting the given values in the equation of motion, we get:

0^2 = 16^2 - 2a(0.4)

Simplifying the above equation, we get:

a = 128 m/s^2

Now, using the formula v = u + at, we can calculate the time taken by the bullet to come to rest:

0 = 16 + (128)t

Simplifying the above equation, we get:

t = 0.125 s

Answer:

Therefore, the time taken during the retardation of the bullet is 0.125 seconds.
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A bullet travelling with a velocity of 16m/s penetrates a tree trunk a...
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Ballistic pendulumThe ballistic pendulum was invented in 1742 by English mathematician Benjamin Robins. A Ballistic Pendulum is a device for measuring a bullet’s momentum and speed by employing perfectly inelastic collision. A large wooden block suspended by two cords serves as the pendulum bob. When a bullet is fired into the bob, it gets embedded in the bob and its momentum is transferred to the bob. The bullet’s momentum and velocity can be determined from the amplitude of the pendulum swing. The velocity of the bullet, in turn, can be derived from its calculated momentum.After collision, if the pendulum reaches a height h, then from principle of conservation of mechanical energywhere,m = mass of bulletM = mass of the bobvP = velocity of the bob-bullet combination∴ Now, Momentum before collision = Momentum after collisionwhere,vB = velocity of bullet∴ The ballistic pendulum used to be a common tool for the determination of the muzzle velocity of bullets as a measure of the performance of firearms and ammunition (Nowadays, the ballistic pendulum. has now been replaced by the ballistic chronograph, an electronic devic e).A ballistic pendulum of 1 kg is fired with a bullet of mass 1 g. If the pendulum rises 2 cm, find the velocity of the bullet.

Ballistic pendulumThe ballistic pendulum was invented in 1742 by English mathematician Benjamin Robins. A Ballistic Pendulum is a device for measuring a bullet’s momentum and speed by employing perfectly inelastic collision. A large wooden block suspended by two cords serves as the pendulum bob. When a bullet is fired into the bob, it gets embedded in the bob and its momentum is transferred to the bob. The bullet’s momentum and velocity can be determined from the amplitude of the pendulum swing. The velocity of the bullet, in turn, can be derived from its calculated momentum.After collision, if the pendulum reaches a height h, then from principle of conservation of mechanical energywhere,m = mass of bulletM = mass of the bobvP = velocity of the bob-bullet combination∴ Now, Momentum before collision = Momentum after collisionwhere,vB = velocity of bullet∴ The ballistic pendulum used to be a common tool for the determination of the muzzle velocity of bullets as a measure of the performance of firearms and ammunition (Nowadays, the ballistic pendulum. has now been replaced by the ballistic chronograph, an electronic devic e).Which two principles of Physics are applied to find the velocity of the bullet?

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A bullet travelling with a velocity of 16m/s penetrates a tree trunk and come to rest in 0.4m.find the time taken during the retardation?
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