Question

1. Ракета,выпущенная вертикально вверх со скоростью 85м/с, попадает в парящий на высоте 300 м планер. Определите скорость, с которой ракета ударилась о планер.

Answer 1

Ответ. h=(v^2)/(2*g); h1=(v^2)/(2*g1); g1=g/6; h1/h=6;

Answer 2

Calculation of the Rocket's Impact Speed

To determine the speed at which the rocket strikes the glider, we can use the principle of conservation of energy. The rocket's initial kinetic energy will be equal to the sum of its final kinetic energy and the potential energy it gains while rising to a height of 300 meters.

Let's assume the mass of the rocket is 'm' and its initial velocity is 85 m/s. The mass of the glider is not given, so we will assume it is negligible compared to the rocket.

The initial kinetic energy of the rocket is given by:

KE_initial = (1/2) * m * (85 m/s)^2

At the maximum height of 300 meters, the rocket will have zero kinetic energy and only potential energy. The potential energy gained by the rocket is given by:

PE_gain = m * g * h

Where 'g' is the acceleration due to gravity (approximately 9.8 m/s^2) and 'h' is the height gained (300 meters).

The final kinetic energy of the rocket just before impact is equal to the potential energy gained:

KE_final = PE_gain = m * g * h

Since the rocket's initial kinetic energy is equal to the sum of its final kinetic energy and the potential energy gained, we can write:

(1/2) * m * (85 m/s)^2 = m * g * h

Simplifying the equation, we can solve for the unknown final velocity 'v':

v = sqrt(85^2 - 2 * g * h)

Now, let's substitute the given values into the equation and calculate the final velocity.

Calculation:

Given: - Initial velocity of the rocket, u = 85 m/s - Height gained by the rocket, h = 300 m - Acceleration due to gravity, g = 9.8 m/s^2

Using the equation: v = sqrt(85^2 - 2 * 9.8 * 300)

Calculating the final velocity 'v':

v = sqrt(7225 - 5880) = sqrt(1345) ≈ 36.7 m/s

Therefore, the speed at which the rocket strikes the glider is approximately 36.7 m/s.