Question

Брошенный мальчиком камень влетел горизонтально в дупло дерева на высоте 7,2м. На каком расстоянии от дерева находился мальчик, если скорость броска 20 м/с? Под каким углом к горизонту был брошен камень? Каково перемещение камня?

Answer 1

Решение смотри на фотографии.

Answer 2

Problem Analysis

We are given the following information: - A stone thrown by a boy enters a tree trunk horizontally at a height of 7.2m. - The throwing speed of the stone is 20 m/s.

We need to determine: 1. The distance from the tree where the boy was standing. 2. The angle at which the stone was thrown. 3. The displacement of the stone.

Distance from the Tree

To find the distance from the tree where the boy was standing, we can use the horizontal motion equation:

distance = speed × time

Since the stone is thrown horizontally, the time taken for the stone to reach the tree is the same as the time taken for the stone to fall vertically from a height of 7.2m. We can use the equation for vertical motion to find the time:

distance = initial velocity × time + (1/2) × acceleration × time^2

In this case, the initial velocity is 0 m/s (since the stone is thrown horizontally) and the acceleration is due to gravity, which is approximately 9.8 m/s^2. The distance is 7.2m. Solving for time:

7.2 = 0 × time + (1/2) × 9.8 × time^2

Simplifying the equation:

4.9 × time^2 = 7.2

time^2 = 7.2 / 4.9

time = sqrt(7.2 / 4.9)

Now that we have the time, we can find the distance from the tree using the horizontal motion equation:

distance = speed × time

Substituting the values:

distance = 20 × sqrt(7.2 / 4.9)

Calculating the value:

distance ≈ 8.28 meters

Therefore, the boy was standing approximately 8.28 meters away from the tree.

Angle of Projection

To find the angle at which the stone was thrown, we can use the equation for the horizontal and vertical components of velocity:

horizontal velocity = speed × cos(angle) vertical velocity = speed × sin(angle)

Since the stone is thrown horizontally, the horizontal velocity is equal to the throwing speed. We can rearrange the equation for horizontal velocity to find the angle:

angle = arccos(horizontal velocity / speed)

Substituting the values:

angle = arccos(20 / 20)

Calculating the value:

angle ≈ 0 degrees

Therefore, the stone was thrown horizontally, so the angle with respect to the horizon is approximately 0 degrees.

Displacement of the Stone

The displacement of the stone is the straight-line distance between the point where it was thrown and the point where it entered the tree trunk. This can be calculated using the Pythagorean theorem:

displacement = sqrt(distance^2 + height^2)

Substituting the values:

displacement = sqrt(8.28^2 + 7.2^2)

Calculating the value:

displacement ≈ 11.02 meters

Therefore, the displacement of the stone is approximately 11.02 meters.

Summary

Based on the given information, we have determined the following: - The boy was standing approximately 8.28 meters away from the tree. - The stone was thrown horizontally, so the angle with respect to the horizon is approximately 0 degrees. - The displacement of the stone is approximately 11.02 meters.

Please note that the calculations provided are based on the given information and assumptions.