Question

Истребитель массой 2,5 т летит со скоростью 396 км/ч. Насколько уменьшится скорость движения самоле- та после 15 с непрерывной стрельбы из автоматичес- кой пушки? Скорострельность пушки — 800 выстрелов в минуту, масса одного снаряда — 100 г, скорость вылета снаряда из пушки — 700 м/с.

Answer 1

Calculation of the Decrease in Speed

To calculate the decrease in speed of the fighter jet after 15 seconds of continuous firing from the automatic cannon, we need to consider the mass of the jet, the rate of fire of the cannon, the mass of each projectile, and the velocity of the projectile.

Given information: - Mass of the fighter jet: 2.5 tons (2,500 kg) - Speed of the fighter jet: 396 km/h (110 m/s) - Rate of fire of the cannon: 800 rounds per minute - Mass of each projectile: 100 grams (0.1 kg) - Velocity of the projectile: 700 m/s

To calculate the decrease in speed, we can use the principle of conservation of momentum. The momentum of the fighter jet before firing is equal to the momentum of the fighter jet and the projectiles after firing.

Conservation of Momentum

The momentum of an object is defined as the product of its mass and velocity. The total momentum before firing is given by:

Initial momentum = (mass of the jet) * (velocity of the jet)

The momentum after firing is given by:

Final momentum = (mass of the jet + mass of the projectiles) * (final velocity)

According to the principle of conservation of momentum, the initial momentum is equal to the final momentum:

(mass of the jet) * (velocity of the jet) = (mass of the jet + mass of the projectiles) * (final velocity)

We can rearrange this equation to solve for the final velocity:

Final velocity = (mass of the jet) * (velocity of the jet) / (mass of the jet + mass of the projectiles)

Calculation

Let's calculate the final velocity of the fighter jet after 15 seconds of continuous firing from the automatic cannon.

First, we need to convert the mass of the jet from tons to kilograms:

Mass of the jet = 2.5 tons = 2,500 kg

Next, we need to calculate the mass of the projectiles fired in 15 seconds:

Mass of the projectiles = (mass of one projectile) * (rate of fire) * (time)

Mass of the projectiles = 0.1 kg * (800 rounds per minute) * (15 seconds / 60 seconds per minute)

Mass of the projectiles = 0.1 kg * (800 / 60) * 15 kg

Mass of the projectiles = 200 kg

Now we can substitute the values into the equation for the final velocity:

Final velocity = (2,500 kg) * (110 m/s) / (2,500 kg + 200 kg)

Final velocity = 275,000 kg·m/s / 2,700 kg

Final velocity ≈ 101.85 m/s

Therefore, the speed of the fighter jet will decrease to approximately 101.85 m/s after 15 seconds of continuous firing from the automatic cannon.

Please note that this calculation assumes no external forces acting on the fighter jet during the firing process and that the mass of the projectiles is negligible compared to the mass of the jet.