Question

З балкона, розміщеного на висоті 20 м, кинули вгору м’яч під кутом 300 до горизонту зі швидкістю 10 м/с. Через який час м’яч упаде на землю?​

Answer 1

Ответ: 2,5 с

Объяснение:Див. додаток

Answer 2

Calculating the Time for the Ball to Fall to the Ground

To calculate the time it takes for the ball to fall to the ground after being thrown from a balcony 20 meters high at an angle of 30 degrees to the horizon with a velocity of 10 m/s, we can use the following steps:

1. Calculate the vertical component of the initial velocity. 2. Use the vertical component of the initial velocity to calculate the time it takes for the ball to reach the maximum height. 3. Use the time calculated in step 2 to calculate the total time for the ball to fall to the ground.

Calculation Steps

1. Calculate the Vertical Component of the Initial Velocity: The vertical component of the initial velocity can be calculated using the formula: \[ v_{i_y} = v_i \cdot \sin(\theta) \] where: - \( v_{i_y} \) = vertical component of the initial velocity - \( v_i \) = initial velocity (given as 10 m/s) - \( \theta \) = angle of 30 degrees

Calculating the vertical component of the initial velocity: \[ v_{i_y} = 10 \cdot \sin(30^\circ) = 10 \cdot 0.5 = 5 \, \text{m/s} \]

2. Calculate the Time to Reach Maximum Height: The time it takes for the ball to reach the maximum height can be calculated using the formula: \[ t_{\text{max}} = \frac{v_{i_y}}{g} \] where: - \( t_{\text{max}} \) = time to reach maximum height - \( v_{i_y} \) = vertical component of the initial velocity (calculated as 5 m/s) - \( g \) = acceleration due to gravity (approximately 9.81 m/s\(^2\))

Calculating the time to reach maximum height: \[ t_{\text{max}} = \frac{5}{9.81} \approx 0.51 \, \text{s} \]

3. Calculate the Total Time for the Ball to Fall to the Ground: Since the motion is symmetrical, the total time for the ball to fall to the ground is twice the time to reach the maximum height. \[ t_{\text{total}} = 2 \times t_{\text{max}} = 2 \times 0.51 = 1.02 \, \text{s} \]

Conclusion

The ball will fall to the ground approximately 1.02 seconds after being thrown from the balcony.