Question

2. Стиснута на 3 см пружина балістичного пістолета жорсткістю 1 кН/м при розпрямленні штовхає "кульку-снаряд" масою 25 гу горизонтальному напрямку. Яка швидкість вильоту "снаряду" і яки час його падіння, якщо дальність польоту по горизонталі 60 см?

Answer 1

Calculation of Projectile Speed and Time of Flight

To calculate the speed of the projectile and the time of flight, we can use the principles of projectile motion. Given that the spring of the ballistic pistol is compressed by 3 cm with a stiffness of 1 kN/m, and the projectile (bullet) has a mass of 25 g, we can find the speed of the projectile and the time of flight.

Calculation Steps:

1. Convert the compressed distance of the spring from centimeters to meters: - 3 cm = 0.03 m

2. Calculate the potential energy stored in the compressed spring: - Potential Energy (PE) = 0.5 * k * x^2 - k: stiffness of the spring (1 kN/m) - x: compressed distance of the spring (0.03 m) - PE = 0.5 * 1 kN/m * (0.03 m)^2

3. Calculate the kinetic energy of the projectile using the potential energy of the spring: - Kinetic Energy (KE) = Potential Energy (PE) - KE = 0.5 * m * v^2 - m: mass of the projectile (25 g = 0.025 kg) - v: velocity of the projectile (unknown) - Substitute the value of PE into the equation: - 0.5 * 1 kN/m * (0.03 m)^2 = 0.5 * 0.025 kg * v^2

4. Solve for the velocity of the projectile (v): - Rearrange the equation to solve for v: - v^2 = (0.5 * 1 kN/m * (0.03 m)^2) / (0.5 * 0.025 kg) - Take the square root of both sides to find v: - v = sqrt((0.5 * 1 kN/m * (0.03 m)^2) / (0.5 * 0.025 kg))

5. Calculate the time of flight (t): - The time of flight can be calculated using the horizontal distance traveled by the projectile. - Given that the horizontal distance is 60 cm = 0.6 m, we can use the equation: - t = d / v - d: horizontal distance traveled by the projectile (0.6 m) - v: velocity of the projectile (calculated in step 4)

Calculation Results:

After performing the calculations, the speed of the projectile (bullet) is approximately 34.64 m/s and the time of flight is approximately 0.0173 seconds.

Please note that these calculations assume ideal conditions and do not take into account factors such as air resistance or other external forces that may affect the actual speed and time of flight of the projectile.