Minimum and terminal velocities in projectile motion

• Main Authors: E.N. Miranda, S. Nikolskaya, R. Riba
• Format: Article
• Language: Portuguese
• Published: Sociedade Brasileira de Física
• Series: Revista Brasileira de Ensino de Física
• Subjects: movimento de projétil; força de arrasto; equação de euler; velocidade terminal
• Online Access: http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172004000200007&lng=en&tlng=en

The motion of a projectile with horizontal initial velocity V0, moving under the action of the gravitational field and a drag force is studied analytically. As it is well known, the projectile reaches a terminal velocity Vterm. There is a curious result concerning the minimum speed Vmin; it turns out that the minimum velocity is lower than the terminal one if V0 > Vterm and is lower than the initial one if V0 < Vterm. These results show that the velocity is not a monotonous function. If the initial speed is not horizontal, there is an angle range where the velocity shows the same behavior mentioned previously. Out of that range, the velocity is a monotonous function. These results comes out from numerical simulations.