Question

Хлопчик кидає м`яч горизонтально з вікна, що розташоване на висоті 20 м від землі. Початкова швидкість руху м`яча 10 м/с. Скільки часу він летітиме до землі? На якій відстані від стіни він впаде? Визначте модуль переміщення м`яча.

Answer 1

Ответ: 20м; 28,28м

Объяснение: путь при свободном падение тела вычисляется по формуле: S=gt², где: g-ускорение свободного падения; t-время падения. Отсюда t=√2S/g=√2*20/10=√4=2с-время падения мяча на землю. Сейчас узнаем какое расстояние пролетит мяч горизонтально: S=V*t=10*2=20м.

Модуль перемещения мяча равен Δr=√h²+l²=√20²+20²=√800=28,28м

Answer 2

Problem Analysis

We have a scenario where a ball is thrown horizontally out of a window located 20 m above the ground. The initial velocity of the ball is 10 m/s. We need to determine the time it takes for the ball to reach the ground, the distance it travels horizontally before hitting the ground, and the magnitude of the ball's displacement.

Solution

To solve this problem, we can use the equations of motion for projectile motion. Since the ball is thrown horizontally, its initial vertical velocity is zero. The only force acting on the ball is gravity, which causes it to accelerate downward at a rate of 9.8 m/s^2.

Time of Flight

The time it takes for the ball to reach the ground can be found using the equation:

time = 2 * (vertical displacement) / (acceleration due to gravity)

In this case, the vertical displacement is the height of the window, which is 20 m, and the acceleration due to gravity is 9.8 m/s^2. Plugging in these values, we get:

time = 2 * 20 m / 9.8 m/s^2

Calculating this, we find that the time of flight is approximately 4.08 seconds.

Horizontal Distance

The horizontal distance traveled by the ball can be found using the equation:

distance = horizontal velocity * time

In this case, the horizontal velocity is the initial velocity of the ball, which is 10 m/s, and the time is the time of flight we calculated earlier. Plugging in these values, we get:

distance = 10 m/s * 4.08 s

Calculating this, we find that the ball will travel approximately 40.8 meters horizontally before hitting the ground.

Magnitude of Displacement

The magnitude of the ball's displacement can be found using the Pythagorean theorem. Since the ball is thrown horizontally, its displacement in the vertical direction is equal to the height of the window, which is 20 m. The displacement in the horizontal direction is equal to the distance traveled by the ball, which is approximately 40.8 m. Using the Pythagorean theorem, we can calculate the magnitude of the displacement:

displacement = sqrt((vertical displacement)^2 + (horizontal displacement)^2)

Plugging in the values, we get:

displacement = sqrt((20 m)^2 + (40.8 m)^2)

Calculating this, we find that the magnitude of the ball's displacement is approximately 45.3 meters.

Summary

To summarize: - The ball will take approximately 4.08 seconds to reach the ground. - It will travel approximately 40.8 meters horizontally before hitting the ground. - The magnitude of the ball's displacement is approximately 45.3 meters.

Please let me know if there is anything else I can help you with!