Question

Шар бросили вертикально вверх на высоту 40м. Определить расстояние, которое он пройдет за первые две секунды движения.

Answer 1

Уравнение движения шара: h=v0t-0.5gt^2;
уравнение скорости шара: v=v0-gt;
В наивысшей точке скорость равна нулю, отсюда найдём время подъёма T.
0=v0-gT;
T=v0/g; Подставим это время в уравнение движения, учитывая, что h(T)=40;
40=v0*(v0/g)-0.5g*(v0/g)^2;
40=(v0^2)/g-0.5(v0^2)/g;
40g=0.5(v0^2);
v0=SQRT(80g);
v0=SQRT(784);
v0=28 (м/с);
получили окончательное уравнение движения:
h=28t-0.5*9.8t^2;
h(2)=28*2-0.5*9.8*2^2;
h(2)=36.4 (м)

Answer 2

Calculation of the Distance Traveled in the First Two Seconds

To determine the distance traveled by the ball in the first two seconds of its motion, we need to consider the vertical motion of the ball when it is thrown vertically upwards.

The key information provided is that the ball is thrown vertically upwards to a height of 40 meters.

To calculate the distance traveled in the first two seconds, we need to consider the motion of the ball during this time period.

The motion of the ball can be divided into two parts: the upward motion and the downward motion.

During the upward motion, the ball is slowing down due to the gravitational force acting against it. At the highest point of its trajectory, the ball momentarily comes to a stop before starting its downward motion.

During the downward motion, the ball accelerates due to the gravitational force acting in the opposite direction.

To calculate the distance traveled in the first two seconds, we need to determine the time it takes for the ball to reach its highest point and then calculate the distance traveled during that time.

Let's break down the calculation step by step:

1. Calculate the time it takes for the ball to reach its highest point: - The time it takes for the ball to reach its highest point can be calculated using the formula: time = (final velocity - initial velocity) / acceleration. - In this case, the initial velocity is the velocity at which the ball is thrown vertically upwards, and the final velocity is 0 m/s at the highest point. - The acceleration is the acceleration due to gravity, which is approximately 9.8 m/s^2. - Plugging in the values, we get: time = (0 - initial velocity) / (-9.8).

2. Calculate the distance traveled during the upward motion: - The distance traveled during the upward motion can be calculated using the formula: distance = initial velocity * time + (1/2) * acceleration * time^2. - In this case, the initial velocity is the velocity at which the ball is thrown vertically upwards, the time is the time calculated in step 1, and the acceleration is the acceleration due to gravity. - Plugging in the values, we get: distance = initial velocity * time + (1/2) * acceleration * time^2.

3. Calculate the distance traveled during the downward motion: - The distance traveled during the downward motion can be calculated using the formula: distance = (initial velocity * time) + (1/2) * acceleration * time^2. - In this case, the initial velocity is 0 m/s at the highest point, the time is the time calculated in step 1, and the acceleration is the acceleration due to gravity. - Plugging in the values, we get: distance = (0 * time) + (1/2) * acceleration * time^2.

4. Add the distances traveled during the upward and downward motions to get the total distance traveled in the first two seconds.

Please note that the initial velocity of the ball when thrown vertically upwards is not provided in the question. Without this information, it is not possible to calculate the exact distance traveled in the first two seconds. If you have the initial velocity, please provide it so that we can proceed with the calculation.