Speed of a Declining Bullet Fired from a Pistol: Calculating Ratio

[autopower99]

what would be the speed of a bullet on decline fired from a pistol. firing angel is 45Deg. What would be the speed of bullet when it reaches 4 feet above from ground during its decline, i just need ratio of firing speed and speed before droping to ground.

 

[tiny-tim]

Welcome to PF!

what would be the speed of a bullet on decline fired from a pistol. firing angel is 45Deg. What would be the speed of bullet when it reaches 4 feet above from ground during its decline, i just need ratio of firing speed and speed before droping to ground.

Hi autopower99! Welcome to PF!

(I assume we're ignoring air resistance?)

The angle doesn't matter.

Just use conservation of energy … KE - mgh = constant.

 

[astrokreng]

The speed of a bullet fired from a pistol is dependent on various factors such as the type of gunpowder used, the weight and shape of the bullet, and the barrel length of the pistol. Therefore, it is not possible to provide a specific speed without knowing these variables.

However, assuming a standard pistol and bullet, the ratio of firing speed and speed before dropping to the ground can be calculated using the principles of projectile motion. The speed of the bullet at the time of firing can be calculated using the formula v = u + at, where v is the final velocity, u is the initial velocity (which is equal to the firing speed in this case), a is the acceleration due to gravity (9.8 m/s^2), and t is the time taken for the bullet to reach its peak height.

At a firing angle of 45 degrees, the time taken for the bullet to reach its peak height is equal to the time taken for it to reach 4 feet above the ground during its decline. This can be calculated using the formula t = u*sin(theta)/g, where theta is the firing angle.

Therefore, the ratio of firing speed and speed before dropping to the ground can be expressed as follows:

Ratio = (u + at)/u

= (u + (u*sin(theta)/g))/u

= (1 + sin(theta)*t*g)/u

= (1 + sin(45)*t*9.8)/u

= (1 + 0.707*t*9.8)/u

Where t is the time taken for the bullet to reach 4 feet above the ground during its decline, and u is the firing speed.

Please note that this is a theoretical calculation and may not accurately reflect the actual speed of the bullet. Various external factors such as air resistance and wind can affect the speed of the bullet in reality. It is always important to handle firearms safely and follow proper shooting protocols.