Question

Ромео в момент часу t=0 c знаходиться в точці x=0м, а його Джульєтта - у точці x=6м. Ромео починає бігти в напряму до неї з постійною швидкістю с 5м/с, але з його коханою щось не так і вона починає тікати від нього з постійним прискоренням a. Знайти таке прискорення дівчини amax при якому Ромео ще зможе її наздогнати.

Answer 1

Відповідь:2$\frac{1}{12}$ м/с²

Пояснення:  (1) -рівняння руху Ромео;  (2) - рівняння руху Джульєтти;  (3) - умова наздоганяння; (4) отримали підставивши (1) і (2) в (3) з врахуванням числових значень. Далі виясняємо при яких а воно має корені.

Answer 2

Problem Analysis

We are given that Romeo starts at position x=0m and Juliet is at position x=6m. Romeo runs towards Juliet with a constant speed of 5m/s, while Juliet starts running away from Romeo with a constant acceleration of a. We need to find the maximum acceleration (amax) at which Romeo can still catch up to Juliet.

Solution

To solve this problem, we can use the equations of motion. Let's assume that Romeo catches up to Juliet at time t. At that moment, the distance covered by Romeo will be equal to the distance covered by Juliet.

Let's break down the problem into two parts: the motion of Romeo and the motion of Juliet.

Motion of Romeo

Romeo runs towards Juliet with a constant speed of 5m/s. The distance covered by Romeo can be calculated using the equation:

Distance covered by Romeo = Speed of Romeo × Time taken by Romeo

Let's denote the time taken by Romeo as tR. Therefore, the distance covered by Romeo is:

Distance covered by Romeo = 5m/s × tR

Motion of Juliet

Juliet starts running away from Romeo with a constant acceleration of a. The distance covered by Juliet can be calculated using the equation of motion:

Distance covered by Juliet = Initial velocity of Juliet × Time taken by Juliet + (1/2) × Acceleration of Juliet × (Time taken by Juliet)^2

Let's denote the initial velocity of Juliet as uJ and the time taken by Juliet as tJ. Therefore, the distance covered by Juliet is:

Distance covered by Juliet = uJ × tJ + (1/2) × a × tJ^2

Equating the Distances

Since Romeo catches up to Juliet, the distance covered by Romeo should be equal to the distance covered by Juliet. Therefore, we can equate the two