Question

сигнальная ракета пущена вертикально вверх со скоростью 30 м в секунду через какой промежуток времени ее скорость уменьшится до 0. на какую высоту за это время поднимается ракета q=10 м/с

Answer 1

Calculation of Time and Height for a Rocket Launched Vertically

To calculate the time it takes for the rocket's velocity to decrease to 0 and the height it reaches during that time, we can use the equations of motion.

Given: - Initial velocity (u) = 30 m/s - Final velocity (v) = 0 m/s - Acceleration (a) = -9.8 m/s^2 (assuming the rocket experiences free-fall acceleration due to gravity) - Initial height (h) = 0 m - Final height (h') = ?

Calculating the Time (t) when the Velocity Decreases to 0

We can use the equation of motion: v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.

Substituting the given values: 0 = 30 + (-9.8)t

Simplifying the equation: -9.8t = -30

Solving for t: t = -30 / -9.8 t ≈ 3.06 seconds

Therefore, it takes approximately 3.06 seconds for the rocket's velocity to decrease to 0.

Calculating the Height (h') Reached by the Rocket

To calculate the height reached by the rocket during this time, we can use the equation of motion: h' = h + ut + (1/2)at^2, where h is the initial height, u is the initial velocity, a is the acceleration, t is the time, and h' is the final height.

Substituting the given values: h' = 0 + (30)(3.06) + (1/2)(-9.8)(3.06)^2

Simplifying the equation: h' = 0 + 91.8 + (-4.9)(9.3636)

Calculating the final height: h' ≈ 91.8 - 45.8 h' ≈ 46 meters

Therefore, during the time it takes for the rocket's velocity to decrease to 0 (approximately 3.06 seconds), the rocket reaches a height of approximately 46 meters.

Please note that the calculations assume no air resistance and that the acceleration due to gravity remains constant throughout the rocket's flight.