Math Problem Statement

Une balle A est lancée vers le haut à partir du sol avec une vitesse v0A de norme v0A. Au bout d’un temps τ, une seconde balle B est lancée vers le bas à une vitesse v0B de norme v0B à partir d’un toit de hauteur H.

Solution

The image you've provided is related to a physics problem involving two balls, A and B, in motion. Let's break it down:

The Setup:

  • Ball A is launched upwards from the ground with an initial velocity vA\vec{v}_A of magnitude v0Av_0A.
  • After a time τ\tau, Ball B is launched downwards from a height HH with an initial velocity vB\vec{v}_B of magnitude v0Bv_0B.

The problem asks you to solve the following:

  1. Determine the equations of motion for both balls (position equations as a function of time).
  2. Find the time and position where the two balls collide.
  3. Find the velocity vectors of both balls at the moment of collision.

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Math Problem Analysis

Mathematical Concepts

Kinematics
Equations of motion
Vector analysis

Formulas

y_A(t) = v0A * t - (1/2) * g * t^2
y_B(t) = H - v0B * t - (1/2) * g * t^2

Theorems

Laws of motion
Free fall

Suitable Grade Level

Grades 9-12