14.7 : Impact: Problem Solving

In an experiment conducted during a Mars mission, a rover propels a projectile with an initial velocity, and the projectile rebounds after colliding with the Martian surface. To ascertain the maximum height attained by the projectile after this collision, the known restitution coefficient and acceleration due to gravity are employed.

By designating the launch point as the origin and utilizing kinematic equations, the vertical component of the projectile's velocity at the point of impact is calculated. In this calculation, upward velocity is considered positive, while the horizontal velocity remains constant. The collision occurs between the incoming projectile and the stationary surface, and the vertical component of the post-collision velocity is determined by incorporating the coefficient of restitution and substituting known values.

As a result, adopting the point of impact as the origin and employing kinematic equations once more, the maximum height reached after the collision is computed. At the zenith of this trajectory, the projectile's vertical velocity is zero. By substituting this zero velocity and the projectile's post-collision velocity into the equation, the projectile's maximum height is then established. This analytical approach allows for a comprehensive understanding of the projectile's motion and trajectory during the Mars mission experiment.