Question

A small cart is rolling at constant velocity vo on a flat track. As it continues to move, a launcher, fixed onto the cart, fires a marble straight up into the air when the end of the launching barrel is passing point i, as shown in the figure. If the launching barrel reaches the position of point ii when the marble returns to the same vertical position that it was launched from, what will be its horizontal position? (Assume air resistance is negligible)

Answer 1

The horizontal position of the marble will be the same as the initial horizontal position when it returns to the same vertical position.

Step-by-step explanation:

In projectile motion, the horizontal and vertical motions are independent of each other. When a cart rolls at a constant velocity on a flat track and a marble is launched vertically upwards from the cart, the horizontal position of the marble when it returns to the same vertical position is the same as its initial horizontal position.

This is because the horizontal velocity of the marble remains constant throughout its motion. Since the cart is moving at a constant velocity, the horizontal position of the marble is determined by the horizontal distance it travels while the cart moves from point i to point ii.

Therefore, the horizontal position of the marble will be the same as the initial horizontal position when it returns to the same vertical position.