Final answer:
To determine the initial acceleration of a ball shot from a compressed air gun at twice its terminal speed, we need to consider the forces acting on the ball. When shot straight up, the net force on the ball is the difference between the downward force of gravity and the upward force from air resistance. When shot straight down, the net force on the ball is the sum of the force of gravity and the force of air resistance.
Step-by-step explanation:
To determine the initial acceleration of a ball shot from a compressed air gun at twice its terminal speed, we need to consider the forces acting on the ball. When shot straight up, gravity acts in the opposite direction of the ball's motion, so the net force on the ball is the difference between the downward force of gravity and the upward force from air resistance. The initial acceleration is determined by dividing this net force by the mass of the ball. Since the ball is shot at twice its terminal speed, we can assume that the net force is twice the magnitude of the force of air resistance at the terminal velocity.
When the ball is shot straight down, the forces acting on the ball are reversed. Gravity acts in the same direction as the ball's motion, so the net force on the ball is the sum of the force of gravity and the force of air resistance. Similarly to the case when the ball is shot straight up, the initial acceleration can be determined by dividing the net force by the mass of the ball. Again, since the ball is shot at twice its terminal speed, we can assume that the net force is twice the magnitude of the force of air resistance at the terminal velocity.