Question

Маленький мячик бросили с земли под углом 60° к горизонту со скоростью 5 м/с в вертикальную стену, расположенную на расстоянии 1,5 м от места бросания. Под каким углом к горизонту отскочит мячик после абсолютно упругого удара о стену?

Answer 1

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Answer 2

Calculation of the Angle of Rebound

To determine the angle at which the ball will rebound off the wall after an elastic collision, we can use the principle of conservation of momentum and the principle of conservation of kinetic energy.

Given: - The ball is thrown from the ground at an angle of 60° to the horizontal. - The initial velocity of the ball is 5 m/s. - The wall is located at a distance of 1.5 m from the point of throwing.

To find the angle of rebound, we need to calculate the angle between the horizontal and the velocity vector of the ball after the collision with the wall.

Let's break down the problem into components and solve it step by step.

Step 1: Initial Velocity Components

The initial velocity of the ball can be broken down into horizontal and vertical components.

The horizontal component of the initial velocity (v₀x) can be calculated using the formula: v₀x = v₀ * cos(θ), where v₀ is the initial velocity of the ball (5 m/s) and θ is the angle of projection (60°).

Substituting the values, we get: v₀x = 5 * cos(60°) = 5 * 0.5 = 2.5 m/s.

The vertical component of the initial velocity (v₀y) can be calculated using the formula: v₀y = v₀ * sin(θ).

Substituting the values, we get: v₀y = 5 * sin(60°) = 5 * 0.866 = 4.33 m/s.

Step 2: Time of Flight

The time of flight (t) can be calculated using the formula: t = 2 * v₀y / g, where g is the acceleration due to gravity (approximately 9.8 m/s²).

Substituting the values, we get: t = 2 * 4.33 / 9.8 = 0.88 s.

Step 3: Horizontal Distance Traveled

The horizontal distance traveled by the ball (R) can be calculated using the formula: R = v₀x * t.

Substituting the values, we get: R = 2.5 * 0.88 = 2.2 m.

Step 4: Distance from the Wall

The distance from the point of throwing to the wall (d) is given as 1.5 m.

Step 5: Angle of Rebound

To find the angle of rebound (θ'), we can use the formula: θ' = arctan(d / R).

Substituting the values, we get: θ' = arctan(1.5 / 2.2) ≈ 34.5°.

Therefore, the ball will rebound off the wall at an angle of approximately 34.5° to the horizontal.

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