Question

Тело брошено под углом 60° к горизонту и дважды находилось на высоте 1 метр над землёй с интервалом в 1 секунду. Определить пройденный путь

Answer 1

Объяснение:

Ответ:

Камень, брошенный под углом 60 градусов к горизонту побывал на высоте 1м дважды с интервалом 1с. Найти начальную скорость и длину полёта.

Вроде решал по инструкции, но решение не логичное выходит.

1) Записать условие задачи

2) Характер движения

3) Указать векторы скорости и ускорения

4) Система отсчёта

5) Нужные кинематические уравнения в векторной и скалярной форме

6) Составить уравнения (систему)

7) Решить

8) Вывод

На рисунках пункты, я делал как надо но ответ не очень выходит.

1)

H=1м

g=10м/c^2

интервал=1с

v0=?

L=?

5)

S=V0t+(gt^2)/2 - векторное уравнение перемещения gx=0 gy=-g

Sx=V0xt - проекция на OX через данное время t

Sy=V0yt-(gt^2)/2 - проекция на OY через данное время t x0=0 y0=0

X=V0xt - координата на OX через данное время t

Y=V0yt-(gt^2)/2 - координата на OY через данное время t

6) По условию видно, что через tс тело имело Y=1м и через (t+1)с Y=1м V0x=V0cos60 V0y=V0sin60:

1=V0sin60t-5t^2

1=V0sin60(t+1)-5(t+1)^2

ПЕРВАЯ СИСТЕМА УРАВНЕНИЙ

Через t1c тело упадёт на землю и будет иметь X=L и Y=0

L=V0cos60*t1

0=V0sin60*t1-5*t1^2

ВТОРАЯ СИСТЕМА УРАВНЕНИЙ

По ним находим v0 и L

Я по этим системам и нахожу v0 и L, но они без смысла - время падения камня выходит 3с, хотя через 3 и 4с тело находилось по полученным данным на 1м Y. Так у меня вопрос - это я совершил ошибку в процессе решения этих уравнений или сами системы уравнения неверно собраны???? /

Answer 2

Problem Analysis

We are given that an object is thrown at an angle of 60° to the horizontal and reaches a height of 1 meter above the ground twice, with a time interval of 1 second. We need to determine the distance traveled by the object.

Solution

To solve this problem, we can break it down into two parts: the horizontal motion and the vertical motion of the object.

# Horizontal Motion

In the horizontal direction, the object moves with a constant velocity. Therefore, the distance traveled horizontally can be calculated using the formula:

Distance = Velocity × Time

Since the velocity is constant, we need to find the horizontal component of the initial velocity.

# Vertical Motion

In the vertical direction, the object moves under the influence of gravity. The motion can be divided into two parts: the upward motion and the downward motion.

During the upward motion, the object slows down due to the gravitational force until it reaches its maximum height. At this point, the vertical component of the velocity becomes zero.

During the downward motion, the object accelerates due to gravity until it reaches the ground again.

We can use the following equations to analyze the vertical motion:

Vertical Displacement = Initial Vertical Velocity × Time + (1/2) × Acceleration × Time^2

Final Vertical Velocity = Initial Vertical Velocity + Acceleration × Time

# Calculation

Let's calculate the distance traveled by the object.

1. Find the horizontal component of the initial velocity: - The initial velocity can be calculated using the formula: Initial Velocity = Total Velocity × cos(Angle) - The total velocity is not given, so we need to find it. We can use the information that the object reaches a height of 1 meter twice, with a time interval of 1 second. - The vertical displacement during the upward motion can be calculated using the formula: Vertical Displacement = Initial Vertical Velocity × Time + (1/2) × Acceleration × Time^2 - Since the object reaches a height of 1 meter twice, we have two equations: 1 = Initial Vertical Velocity × 1 + (1/2) × Acceleration × 1^2 1 = Initial Vertical Velocity × 2 + (1/2) × Acceleration × 2^2 - Solving these equations simultaneously will give us the values of Initial Vertical Velocity and Acceleration. - Once we have the values of Initial Vertical Velocity and Acceleration, we can calculate the horizontal component of the initial velocity using the formula: Initial Velocity = Total Velocity × cos(Angle) - The angle is given as 60°, so we can calculate the horizontal component of the initial velocity.

2. Calculate the time taken for the object to reach the maximum height: - The time taken for the object to reach the maximum height can be calculated using the formula: Final Vertical Velocity = Initial Vertical Velocity + Acceleration × Time - Since the final vertical velocity at the maximum height is zero, we can set the equation to zero and solve for time.

3. Calculate the time taken for the object to reach the ground again: - The time taken for the object to reach the ground again can be calculated using the formula: Vertical Displacement = Initial Vertical Velocity × Time + (1/2) × Acceleration × Time^2 - Since the vertical displacement is equal to the initial height (1 meter), we can set the equation to 1 and solve for time.

4. Calculate the distance traveled horizontally: - Now that we have the horizontal component of the initial velocity and the time taken for the object to reach the ground again, we can calculate the distance traveled horizontally using the formula: Distance = Velocity × Time

Let's perform the calculations step by step.

Calculation

1. Find the horizontal component of the initial velocity: - The total velocity can be calculated using the information that the object reaches a height of 1 meter twice, with a time interval of 1 second. - The vertical displacement during the upward motion can be calculated using the formula: Vertical Displacement = Initial Vertical Velocity × Time + (1/2) × Acceleration × Time^2 - Since the object reaches a height of 1 meter twice, we have two equations: 1 = Initial Vertical Velocity × 1 + (1/2) × Acceleration × 1^2 1 = Initial Vertical Velocity × 2 + (1/2) × Acceleration × 2^2 - Solving these equations simultaneously will give us the values of Initial Vertical Velocity and Acceleration. - Once we have the values of Initial Vertical Velocity and Acceleration, we can calculate the horizontal component of the initial velocity using the formula: Initial Velocity = Total Velocity × cos(Angle) - The angle is given as 60°, so we can calculate the horizontal component of the initial velocity.

2. Calculate the time taken for the object to reach the maximum height: - The time taken for the object to reach the maximum height can be calculated using the formula: Final Vertical Velocity = Initial Vertical Velocity + Acceleration × Time - Since the final vertical velocity at the maximum height is zero, we can set the equation to zero and solve for time.

3. Calculate the time taken for the object to reach the ground again: - The time taken for the object to reach the ground again can be calculated using the formula: Vertical Displacement = Initial Vertical Velocity × Time + (1/2) × Acceleration × Time^2 - Since the vertical displacement is equal to the initial height (1 meter), we can set the equation to 1 and solve for time.

4. Calculate the distance traveled horizontally: - Now that we have the horizontal component of the initial velocity and the time taken for the object to reach the ground again, we can calculate the distance traveled horizontally using the formula: Distance = Velocity × Time

Let's perform the calculations step by step.

Calculation

1. Find the horizontal component of the initial velocity: - The total velocity can be calculated using the information that the object reaches a height of 1 meter twice, with a time interval of 1 second. - The vertical displacement during the upward motion can be calculated using the formula: Vertical Displacement = Initial Vertical Velocity × Time + (1/2) × Acceleration × Time^2 - Since the object reaches a height of 1 meter twice, we have two equations: 1 = Initial Vertical Velocity × 1 + (1/2) × Acceleration × 1^2 1 = Initial Vertical Velocity × 2 + (1/2) × Acceleration × 2^2 - Solving these equations simultaneously will give us the values of Initial Vertical Velocity and Acceleration. - Once we have the values of Initial Vertical Velocity and Acceleration, we can calculate the horizontal component of the initial velocity using the formula: Initial Velocity = Total Velocity × cos(Angle) - The angle is given as 60°, so we can calculate the horizontal component of the initial velocity.

2. Calculate the time taken for the object to reach the maximum height: - The time taken for the object to reach the maximum height can be calculated using the formula: Final Vertical Velocity = Initial Vertical Velocity + Acceleration × Time - Since the final vertical velocity at the maximum height is zero, we can set the equation to zero and solve for time.

3. Calculate the time taken for the object to reach the ground again: - The time taken for the object to reach the ground again can be calculated using the formula: Vertical Displacement = Initial Vertical Velocity × Time + (1/2) × Acceleration × Time^2 - Since the vertical displacement is equal to the initial height (1 meter), we can set the equation to 1 and solve for time.

4. Calculate the distance traveled horizontally: - Now that we have the horizontal component of the initial velocity and the time taken for the object to reach the ground again, we can calculate the distance traveled horizontally using the formula: Distance = Velocity × Time

Let's perform the calculations step by step.

Calculation

1. Find the horizontal component of the initial velocity: - The total velocity can be calculated using the information that the object reaches a height of 1 meter twice, with a time interval of 1 second. - The vertical displacement during the upward motion can be calculated using the formula: Vertical Displacement = Initial Vertical Velocity × Time + (1/2) × Acceleration × Time^2 - Since the object reaches a height of 1 meter twice, we have two equations: 1 = Initial Vertical Velocity × 1 + (1/2) × Acceleration × 1^2 1 = Initial Vertical Velocity × 2 + (1/2) × Acceleration × 2^2 - Solving these equations simultaneously will give us the values of Initial Vertical Velocity and Acceleration. - Once we have the values of Initial Vertical Velocity and Acceleration, we can calculate the horizontal component of the initial velocity using the formula: Initial Velocity = Total Velocity × cos(Angle) - The angle is given as 60°, so we can calculate the horizontal component of the initial velocity.

2. Calculate the time taken for the object to reach the maximum height: - The time taken for the object to reach the maximum height can be calculated using the formula: Final Vertical Velocity = Initial Vertical Velocity + Acceleration × Time - Since the final vertical velocity at the maximum height is zero, we can set the equation to zero and solve for time.

3. Calculate the time taken