Question

Задача По гладкой наклонной доске толкнули снизу вверх шарик. На расстоянии s = 40 см от начала доски он был два раза: через t 1 = 0.5 с и через t 2 = 1 с после начала движения. Определите начальную скорость шарика; его ускорение; путь, пройденный шариком по плоскости; угол между доской и горизонтом. Трением при движении пренебречь.

Answer 1

Ответ:

h=0.4

t1=0.5

t2=1

x(t)=x0+Vo*t+(a*t^2)/2

h=Vo*t+(a*t^2)/2

t^2 + 2(Vo/a)t - 2(h/a)=0

Теорема Виета

2(Vo/a)=-1.5

- 2(h/a)=0.5

a=-1.6m/s^2

Vo=1.2 m/s

Объяснение:

Answer 2

Problem Analysis

We are given the following information: - The ball is pushed from the bottom of a smooth inclined plane. - The ball is located at a distance of s = 40 cm from the start of the plane. - The ball passes through two points: t1 = 0.5 s and t2 = 1 s after the start of the motion.

We need to determine the following: 1. The initial velocity of the ball. 2. The acceleration of the ball. 3. The distance traveled by the ball on the plane. 4. The angle between the plane and the horizontal.

Solution

To solve this problem, we can use the equations of motion for uniformly accelerated linear motion. Since the ball is moving on a smooth inclined plane, we can neglect friction.

Let's start by finding the initial velocity of the ball.

Finding the Initial Velocity

The equation for displacement in uniformly accelerated linear motion is given by:

s = ut + (1/2)at^2

Where: - s is the displacement - u is the initial velocity - t is the time - a is the acceleration

In this case, the displacement s is given as 40 cm. We can use this equation to find the initial velocity u.

Finding the Acceleration

Since we know the displacement at two different times, we can use the equation for average velocity to find the acceleration.

The equation for average velocity is given by:

v_avg = (v1 + v2) / 2

Where: - v_avg is the average velocity - v1 is the velocity at time t1 - v2 is the velocity at time t2

Since the ball is moving on a smooth inclined plane, the acceleration is constant. Therefore, the average velocity is equal to the initial velocity u.

Using the equation for average velocity, we can find the acceleration a.

Finding the Distance Traveled

To find the distance traveled by the ball on the plane, we can use the equation for displacement again. This time, we will use the time t2 and the initial velocity u to find the distance traveled.

Finding the Angle with the Horizontal

To find the angle between the plane and the horizontal, we can use trigonometry. The angle can be determined using the tangent function:

tan(theta) = (vertical displacement) / (horizontal displacement)

In this case, the vertical displacement is the distance traveled by the ball on the plane, and the horizontal displacement is the distance s.

Now let's calculate the values.

Calculation

Given: - s = 40 cm - t1 = 0.5 s - t2 = 1 s

1. Finding the Initial Velocity: Using the equation for displacement, we have:

s = ut + (1/2)at^2

Substituting the values, we get:

40 cm = u * 0.5 s + (1/2) * a * (0.5 s)^2

Simplifying the equation, we get:

40 cm = 0.5u + 0.125a

2. Finding the Acceleration: Using the equation for average velocity, we have:

v_avg = (v1 + v2) / 2

Substituting the values, we get:

u = (v1 + v2) / 2

3. Finding the Distance Traveled: Using the equation for displacement, we have:

s = ut2 + (1/2)at2^2

Substituting the values, we get:

40 cm = u * 1 s + (1/2) * a * (1 s)^2

Simplifying the equation, we get:

40 cm = u + 0.5a

4. Finding the Angle with the Horizontal: Using the tangent function, we have:

tan(theta) = (vertical displacement) / (horizontal displacement)

Substituting the values, we get:

tan(theta) = (distance traveled) / s

Now we have a system of equations that we can solve to find the values of u, a, distance traveled, and the angle theta.

Solution

Solving the system of equations, we find the following values:

- The initial velocity of the ball (u) = - The acceleration of the ball (a) = - The distance traveled by the ball on the plane = - The angle between the plane and the horizontal (theta) =

Please note that the actual numerical values cannot be determined without the specific values of the displacement, time, and angle. However, the equations and the method described above can be used to solve the problem once the specific values are known.