Air resistance slows the ball down, so its acceleration (a) is less than gravity (g). Option (C) best shows this: a < g. Option C is correct.
The question is asking which of the following best shows the magnitude and the direction of the ball's acceleration at time t. The image shows the ball moving up and to the right at an angle of 45 degrees to the horizontal.
The answer is (C), a < g.
This is because air resistance is acting on the ball in the opposite direction of its motion, which is slowing it down. Therefore, the acceleration of the ball is less than g.
The other options are incorrect because they either do not account for air resistance, or they indicate that the acceleration is greater than g.
The vector g represents the acceleration due to gravity, which is always acting downwards. The vector v represents the velocity of the ball, which is angled upwards and to the right. The vector F represents the force of air resistance, which is acting in the opposite direction of the ball's motion. The vector a represents the acceleration of the ball, which is less than g due to air resistance.