chapter 3 two-dimensional kinematics

Two-dimensional motion

Can be broken into horizontal and vertical components, which are independent of each other.

Total distance walked in the city problem

14 blocks.

Straight-line distance in the city problem

10.3 blocks, calculated using the Pythagorean theorem.

Head-to-tail method

A graphical method for adding vectors by positioning the tail of one vector at the head of another.

Negative vector

A vector with the same magnitude as another vector but in the opposite direction.

Resultant magnitude formula for perpendicular vectors

R = √(A² + B²) using the Pythagorean theorem.

Resultant direction formula

θ = tan⁻¹(B/A).

Projectile motion acceleration

Constant downward acceleration due to gravity, g = 9.8 m/s².

Component equations

For a vector A at angle θ: Aₓ = A cos θ; Aᵧ = A sin θ.

Range equation for projectile on level ground

R = (v₀² sin(2θ))/g, where R is the horizontal range.

Orbital principle

An object in orbit falls continuously but never hits the surface because the Earth curves away.

Relative velocity equation

vₐ𝒸 = vₐ𝒃 + v𝒃𝒸, where subscripts denote the reference frames.

Classic relativity principle

Different observers may describe the same motion differently based on their reference frames.

Maximum projectile range

Occurs at launch angle θ = 45°.

Velocity component equations

vₓ = v cos θ, vᵧ = v sin θ, used to analyze 2D motion.

Pythagorean theorem

Used to find the resultant magnitude in vector addition for perpendicular components.