Question

Стрела выпущена с ровной горизонтальной земли пол углом 60 градусов к горизонту. В момент, когда она прошла половину пути, её скорость равна 35м/с. Какова начальная скорость тела?

Answer 1

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Answer 2

Calculation of the Initial Velocity of the Projectile

To determine the initial velocity of the projectile, we can use the information provided. The arrow is launched from a flat horizontal surface at an angle of 60 degrees to the horizon. When it has traveled half of its total distance, its velocity is measured to be 35 m/s.

To solve this problem, we can use the equations of motion for projectile motion. The horizontal and vertical components of the initial velocity can be calculated separately.

Let's denote the initial velocity of the arrow as V0, the time taken to reach half of the total distance as t, and the acceleration due to gravity as g (which is approximately 9.8 m/s^2).

Calculation of the Horizontal Component of the Initial Velocity

The horizontal component of the initial velocity remains constant throughout the motion. Therefore, we can use the equation:

Horizontal distance = Horizontal component of initial velocity × time

Since the arrow has traveled half of the total distance, the horizontal distance is half of the total distance. Let's denote the total distance as d.

d/2 = V0 × cos(60) × t

Calculation of the Vertical Component of the Initial Velocity

The vertical component of the initial velocity changes due to the acceleration due to gravity. We can use the equation:

Vertical distance = Vertical component of initial velocity × time + (1/2) × g × t^2

Since the arrow has traveled half of the total distance, the vertical distance is half of the total distance. Let's denote the total distance as d.

(d/2) = V0 × sin(60) × t - (1/2) × g × t^2

Solving the Equations

We have two equations, and with two unknowns: V0 and t. We can solve these equations simultaneously to find the values of V0 and t.

However, since we are only interested in finding the initial velocity, we can simplify the problem by eliminating t from the equations.

From equation we can express t in terms of V0:

t = (d/2) / (V0 × cos(60)) Substituting equation into equation we can solve for V0:

(d/2) = V0 × sin(60) × [(d/2) / (V0 × cos(60))] - (1/2) × g × [(d/2) / (V0 × cos(60))]^2

Simplifying the equation:

(d/2) = (d/2) × tan(60) - (1/2) × g × [(d/2) / (V0 × cos(60))]^2

Simplifying further:

1 = tan(60) - (1/2) × g × [(d/2) / (V0 × cos(60))]^2

Now, we can solve this equation to find the value of V0.

Calculation Result

Using the given information, we can substitute the values into the equation and solve for V0.

Please provide the value of the total distance d in meters, and I will calculate the initial velocity V0 for you.