A bullet is fired from the cart vertically at the same instant cart begins to accelerate forward. Which of the following best describes the subsequent motion of the bullet?
A. The bullet goes up and then straight back down into the cart
B. The bullet goes up and lands in front of the cart
C. The bullet goes up and lands behind the cart
D. The bullet stops in the air as the cart is accelerating and “floats” until the cart stops accelerating
E. The bullet goes up and to the right to the cart.

Hint: Since we have to observe the motion of the bullet with respect to the cart, we will only consider the horizontal component of the bullet's motion. When the bullet is fired vertically upwards. Then the horizontal motion of the bullet will be zero.

Complete step by step answer:
1) As we know that a bullet is fired from the cart vertically.
2) The cart begins to travel in the forward direction at the same time.
3) Now, as the bullet is fired upwards, the horizontal displacement of the bullet will be zero.
Since, the horizontal component of displacement of the bullet is zero. The bullet will not travel any distance in the forward direction. And hence, it will fall behind the cart as the cart has been moved forward by the time the bullet comes back to the ground.
Hence, from the above explanation, the correct option is (C) the bullet goes up and lands behind the cart.

So, the correct answer is “Option C”.

Note:
It may be noted that the bullet will have sufficient velocity to travel in the vertical direction. So do not assume that the bullet will fall back on the ground before the cart could move from the position under it. We might think that the speed of the bullet will be too high in comparison to the cart and hence the bullet will fall back on the cart itself. That would be a wrong answer. We are studying simple laws of physics with simple applications. So do not try to engage into such possibilities. You would get wrong answers. Keep concepts simple and be practical.