Question

Тела А и В движутся навстречу друг другу по одной вертикали. Тело А брошено вертикально вверх с начальной скоростью (v0)1=25 м/с,тело В падает с высоты H(23м) и начальной скоростью (v0)2=0. тела начали двигаться одновременно и через время t(0.32 с) расстояние между ними стало равным h. Определить время, спустя которое тела встретятся.

Answer 1

время до встречи 0,92с. h1=v0-gt^2/2. h2=gt^2/2. где t=0,32. а v0=25 h1=25*0,32-(10*0,32^2)/2=7,488 h2=(10*0,32^2 )/2=0,512 h=23- 7,488-0,512=15

Answer 2

Problem Analysis

We are given two bodies, A and B, moving towards each other along a vertical line. Body A is thrown vertically upwards with an initial velocity of 25 m/s, while body B falls from a height of 23 m with an initial velocity of 0 m/s. After a certain time, the distance between them becomes h. We need to determine the time it takes for the bodies to meet.

Solution

To solve this problem, we can use the equations of motion for each body and equate their positions to find the time of intersection.

Let's start by analyzing the motion of each body separately.

For body A: - Initial velocity (v0) = 25 m/s - Acceleration due to gravity (g) = 9.8 m/s^2 (assuming standard gravity) - Initial position (h0) = 0 (since it is thrown vertically upwards)

For body B: - Initial velocity (v0) = 0 m/s - Acceleration due to gravity (g) = 9.8 m/s^2 (assuming standard gravity) - Initial position (h0) = 23 m

Now, let's calculate the time it takes for body A to reach the height h and the time it takes for body B to fall from a height of 23 m.

Using the equation of motion for vertical motion: h = h0 + v0t + (1/2)gt^2

For body A: h = 0 + (25)t - (1/2)(9.8)t^2

For body B: h = 23 + 0t - (1/2)(9.8)t^2

Now, let's equate the positions of body A and body B to find the time of intersection.

0 + (25)t - (1/2)(9.8)t^2 = 23 + 0t - (1/2)(9.8)t^2

Simplifying the equation, we can see that the terms involving t^2 cancel out:

25t = 23

Solving for t, we find:

t = 23 / 25 = 0.92 seconds

Therefore, the bodies will meet after approximately 0.92 seconds.

Answer

The bodies A and B will meet approximately 0.92 seconds after they start moving towards each other.

Note: The above solution assumes standard gravity (9.8 m/s^2) and neglects air resistance.