The 1-D equations are modified simply by adding an x or y subscript to all the vector variables. As in 1-D, the equations apply under the following conditions:

• the acceleration is constant
• the motion is measured from t = 0
• plus and minus signs give directions for the vector components

There is a similar set of equations for the y-direction. Simply replace all the x's by y's in the equations above.

IMPORTANT: When solving problems always keep the x-component data separate from the y-component data. The only thing that can be used in both sets of equations is time.

Two balls are launched simultaneously from the same height. Ball A is released from rest, and drops straight down. Ball B is given an initial horizontal velocity.

Which ball hits the ground first?

1. Ball A
2. Ball B
3. Both balls hit the ground at the same time

Both balls hit the ground at the same time. This is because the vertical motion is completely independent of the horizontal motion.

A ballistic cart is a cart that can shoot a ball vertically and (maybe) catch it again.

With the cart rolling at constant speed when it shoots the ball, where will the ball land?

1. In the cart
2. Behind the cart
3. Ahead of the cart

Both the ball and the cart have the same x-position at all times, so the ball must land back in the cart. The ball's x-velocity is not affected by its motion in the y direction.