# Motion in two dimensions

Experiments show that motion in two perpendicular directions are independent - one does not affect the other. The classic demonstration of this is shooting a ball horizontally toward a falling light bulb. If they both go at the same time from the same height, the ball can't miss the bulb. The key to understanding this is that the horizontal motion of the ball does not affect its vertical motion. The vertical motions of the ball and light bulb are identical.

## River Crossing Problem

Consider a boat being rowed straight across a river. The speed of the boat is 2 m/s while the speed of the river is 3 m/s. The river is 200 m wide.

a) How long will it take to cross the river?

```  The motion across the river is independent of the motion downstream, so we just do
d = vt
200 = 2t which solves to t = 100 s.
```

b) How far does the boat get carried downstream while crossing the river?

```  d = vt = 3(100) = 300 m.
```

## Projectile Motion

When gravity is the only force acting on an object, the object is considered to be a projectile. Projectiles can be any object such as bullets, footballs, or humans. It is standard practice when analyzing projectile motion to seperate the two dimensional problem into two one dimensional problems, analyze the motion in the horizontal direction, analyze the motion in the vertical direction, and then combine the results.

Consider a baseball thrown at an angle of 30 degrees above horizontal and an initial speed of 15 m/s. Find the maximum height, time of flight and horizontal distance of flight.

## Inclined Planes

On a ramp, the interesting directions are along the ramp and straight into the ramp. The gravitational force (weight) is straight down, but we must separate it into a component along the ramp (F parallel or F[sub]//[/sub]) and a component into the ramp (normal force, Fn). Consider a box with mass 100 kg on a ramp. The coefficient of friction between the ramp and the box is 0.1. With what acceleration will it slide along the ramp?