A ball is launched with initial velocity components v_x = 10 m/s and v_y = 20 m/s. After 2 seconds (ignoring air resistance, with g = 10 m/s²), what is the horizontal velocity?
A0 m/s
B10 m/s
C20 m/s
DIt depends on the vertical motion
Horizontal and vertical motions are independent. With no horizontal acceleration, v_x remains constant at 10 m/s throughout the motion. The vertical velocity changes (v_y = 20 - 10×2 = 0 m/s at t = 2 s), but this has no effect on the horizontal component.
Question 2 True / False
Solving a 2D kinematics problem requires new equations that are different from the 1D kinematic equations.
TTrue
FFalse
Answer: False
This is a common misconception. 2D kinematics uses exactly the same equations as 1D kinematics — they are simply applied separately to the x and y components. The only new technique is decomposing vectors into components before applying the familiar equations. The two component equations are linked by the shared time variable t.
Question 3 Short Answer
An object is launched at an angle θ above the horizontal with speed v₀. Describe the first step in setting up the kinematic equations for its motion.
Think about your answer, then reveal below.
Model answer: Decompose the initial velocity into components: v₀ₓ = v₀ cos θ (horizontal) and v₀ᵧ = v₀ sin θ (vertical). Then apply the 1D kinematic equations separately to each component, using the same time t in both.
The decomposition step is essential because the kinematic equations operate on scalar components along a single axis. Once you have v₀ₓ and v₀ᵧ, the x-direction has constant velocity (no horizontal acceleration in free flight) and the y-direction has constant acceleration −g. The time t links the two equations and is usually the key variable to eliminate or solve for.