Question

Тело массы 3 кг брошенное вертикально вверх со скоростью V 15 м/с преодолевает силу сопротивления среды R котрая линейно зависит от скорости( R = 0.6*V). через какое время тело достигнет наивысшей точки

Answer 1

На тело действуют три силы

1) Сила, с которой бросили тело F=ma

2) Сила тяжести ( в обратную сторону ) Fт=mg

3) Сила сопротивления среды R = 0.6*V

ma = mg+0.6v

3a=30+9

a=13 м/с²

v=v0+at

В наивысшей точке скорость тела = 0

Значит, 0=15+13t ⇒ 13t=-15 ⇒ t=15/13≈1.15 c

Answer 2

Calculation of the Time to Reach the Highest Point

To calculate the time it takes for the object to reach the highest point, we need to consider the forces acting on the object. In this case, we have the force of gravity pulling the object downward and the force of air resistance opposing its motion.

Given: - Mass of the object (m) = 3 kg - Initial velocity (V) = 15 m/s - Air resistance force (R) = 0.6 * V

To find the time it takes for the object to reach the highest point, we can use the following steps:

1. Determine the net force acting on the object at the highest point. At the highest point, the object momentarily comes to rest, so the net force is zero. 2. Equate the forces acting on the object to find the net force equation. 3. Solve the net force equation to find the time it takes for the object to reach the highest point.

Step 1: Determine the Net Force at the Highest Point

At the highest point, the net force acting on the object is zero. This means that the force of gravity is equal to the force of air resistance:

Force of gravity = Force of air resistance

Step 2: Equate the Forces

The force of gravity can be calculated using the formula:

Force of gravity = mass * acceleration due to gravity

The force of air resistance is given as:

Force of air resistance = R = 0.6 * V

Equating the forces, we have:

mass * acceleration due to gravity = 0.6 * V

Step 3: Solve for Time

We can rearrange the equation to solve for the acceleration due to gravity:

acceleration due to gravity = (0.6 * V) / mass

The acceleration due to gravity is constant and equal to approximately 9.8 m/s^2.

Using the equation of motion for vertical motion:

Final velocity (Vf) = Initial velocity (Vi) + acceleration * time

At the highest point, the final velocity is zero, so we have:

0 = V + (-9.8) * time

Solving for time:

time = -V / (-9.8)

Substituting the given values:

time = -15 / (-9.8)

Calculating the value, we find:

time ≈ 1.53 seconds

Therefore, it will take approximately 1.53 seconds for the object to reach the highest point.

Please note that the negative sign in the equation indicates that the object is moving in the opposite direction of the positive vertical axis.