Question

Пуля,летящая со скоростью 400 м/с ,ударяется о земляной вал и проникает в него на глубину 36 см. Cколько времени двигалась пуля внутри вала? с каким ускорением? какова была скорость пули на глубине 18 см? на какой глубине скорость пули уменьшилась в 3 раза?

Answer 1

Дано
v0 =400 м/с
vк = 0
d = 36 см =0.36 м
d1 = 18 см = 0.18 м
n=v0/v(n) =3
-------
t - ?
a - ?
v(18) - ?
d(n) - ?
РЕШЕНИЕ
движение равнозамедленное
средняя скорость Vcp = (v0+v) /2 = (400+0) /2 = 200 м/с
время движения t = d/Vcp =0.36/200 =0,0018 c = 1.8 мс
ускорение a = (v- v0) /t = (0-400) / 0.0018 = - 222222,22 м/с2
скорость пули на глубине 18 см :  
d1 = (v(18)^2 -v0^2) / 2a
v(18) = √(2ad1 +v0^2) =√(2 * - 222222.22*0.18 +400^2) = 282.84 м/с
v(n) = v0/3
d(n) = (v(n)^2 -v0^2) / 2a = (1/9 v0^2 -v0^2) / 2a = -8v0^2 / 18a = 
      = -8*400^2 / 18*(- 222222.22) = 0.32 м = 32 см
ОТВЕТ 1.8 с ; - 222222 м/с2 ;282.84 м/с ;32 см

Answer 2

Calculation of Time and Acceleration

To calculate the time the bullet was moving inside the wall, we can use the formula:

time = distance / velocity

Given that the bullet penetrates the wall to a depth of 36 cm and has a velocity of 400 m/s, we can calculate the time as follows:

time = 0.36 m / 400 m/s

Calculating this, we find that the bullet was moving inside the wall for approximately 0.0009 seconds.

To calculate the acceleration of the bullet, we can use the formula:

acceleration = change in velocity / time

Since we don't have information about the change in velocity, we cannot calculate the acceleration.

Calculation of Bullet's Velocity at a Depth of 18 cm

To calculate the bullet's velocity at a depth of 18 cm, we can assume that the bullet's deceleration is constant throughout its penetration. In this case, we can use the equation of motion:

final velocity^2 = initial velocity^2 + 2 * acceleration * distance

Given that the initial velocity is 400 m/s and the distance is 18 cm, we can calculate the final velocity as follows:

final velocity^2 = 400^2 + 2 * acceleration * 0.18

Unfortunately, without information about the acceleration, we cannot calculate the bullet's velocity at a depth of 18 cm.

Calculation of Depth at which the Bullet's Velocity Decreased by 3 Times

To calculate the depth at which the bullet's velocity decreased by 3 times, we need to find the point where the velocity is one-third of the initial velocity.

Using the same equation of motion as before, we can solve for the distance:

final velocity^2 = initial velocity^2 + 2 * acceleration * distance

Given that the initial velocity is 400 m/s and the final velocity is one-third of the initial velocity (400 m/s / 3), we can calculate the distance as follows:

(400/3)^2 = 400^2 + 2 * acceleration * distance

Unfortunately, without information about the acceleration, we cannot calculate the depth at which the bullet's velocity decreased by 3 times.

Please note that the calculations above assume certain simplifications and ideal conditions. In reality, factors such as air resistance, deformation of the bullet, and other variables may affect the actual results.