# AP Physics C: Mechanics : Calculating Motion in Two Dimensions

## Example Questions

### Example Question #14 : Mechanics Exam

ball is thrown horizontally from the top of a  high building. It has an initial velocity of  and lands on the ground  away from the base of the building. Assuming air resistance is negligible, which of the following changes would cause the range of this projectile to increase?

I. Increasing the initial horizontal velocity

II. Decreasing the mass of the ball

III. Throwing the ball from an identical building on the moon

I and II

II only

I only

I, II, and III

I and III

I and III

Explanation:

Relevant equations:

Choice I is true because  is proportional to the range , so increasing  increases  if  is constant. This relationship is given by the equation:

Choice II is false because the motion of a projectile is independent of mass.

Choice III is true because the vertical acceleration on the moon  would be less. Decreasing  increases the time the ball is in the air, thereby increasing  if  is constant. This relationship is also shown in the equation:

### Example Question #1 : Calculating Motion In Two Dimensions

Water emerges horizontally from a hole in a tank  above the ground. If the water hits the ground  from the base of the tank, at what speed is the water emerging from the hole? (Hint: Treat the water droplets as projectiles.)

Explanation:

To understand this problem, we have to understand that the water has a x-velocity and a y-veloctiy. The x-velocity never changes.

First we want to find the time it took for the water to hit the ground. We can use this equation:

We know that the y-velocity is 0 to start with, acceleration is  and .

Substituting into the equation, we get:

Next we have to substitute the time into the equation for the x component

We know that  and , so we can conclude that: