# Physics Exercises/Kinematics in 2-3 Dimensions

**Kinematics in 2 or 3 dimensions** is essentially the same as Kinematics in One Dimension with an extra step added: one must separate the motion into 2 or 3 perpendicular directions (for each problem, one particular choice of axes is better than others) and solve motion in each direction separately as it is done in Kinematics in One Dimension.

## Without Calculus[edit]

- A cannon (assumed to be at ground level) is fired off a flat surface at an angle
*θ*above the horizontal with an initial speed of . Assume no air resistance.- What is the initial horizontal component of the velocity?
- What is the initial vertical component of the velocity?
- What is the horizontal component of the velocity at the highest point of the trajectory?
- What is the vertical component of the velocity at that point?
- What is the horizontal component of the velocity when the projectile lands?
- What is the vertical component of the velocity when it lands?

- A woman walks north at 3 km/h on a boat that is moving east at 4 km/h.
- With respect to the shore, how fast is the woman moving?
- With respect to the shore, at what angle from the north is she moving?

## With Calculus[edit]

- Just for this problem, assume
*t*is a unitless quantity measuring time. A cockroach has a velocity . The cockroach starts at the origin. Derive an expression for- the speed of the cockroach as a fuction of time,
- the position of the cockroach as a function of time,
- the acceleration of the cockroach as a function of time.