CourseCourseQuestionQuestionDocumentDocument

A.1.8—Projectile components

Syllabus
First assessment 2025
Objective
—
Level
HL

Resolve Projectile Motion into Components

Separate the axes

With negligible fluid resistance, projectile motion is independent horizontal and vertical motion. Resolve the launch velocity:

ux=ucos⁡θ,uy=usin⁡θu_x=u\cos\theta,\qquad u_y=u\sin\theta

Horizontal motion

There is no horizontal acceleration in the ideal model, so vx=uxv_x=u_x and x=uxtx=u_xt. Use the horizontal displacement to find time or horizontal speed.

Vertical motion

Use one-dimensional constant-acceleration equations vertically, usually with ay=−ga_y=-g if upward is positive. The horizontal and vertical equations share the same time tt.

Worked example from local Question Bank row 31723

A tennis ball travels 11.9 m11.9\,\mathrm{m} horizontally after launch at 64.0 m s−164.0\,\mathrm{m\,s^{-1}} and 7∘7^\circ to the horizontal.

ux=64.0cos⁡7∘=63.52 m s−1u_x=64.0\cos7^\circ=63.52\,\mathrm{m\,s^{-1}}
t=xux=11.963.52=0.187 st=\frac{x}{u_x}=\frac{11.9}{63.52}=0.187\,\mathrm{s}

The same 0.187 s0.187\,\mathrm{s} must then be used in the vertical equation.

Common trap

Do not use the launch speed as the horizontal speed. Resolve it first, and do not use the horizontal time independently of the vertical motion.

A.1.8 Exam Analysis

[ 2 ]

The ball leaves the ground at an angle of 22∘22^{\circ}. The horizontal distance from the initial position of the edge of the ball to the wall is 11 m . Calculate the time taken for the ball to reach the wall.

Retrieve the A.1 Kinematics Model

Describe motion

Position locates the object, velocity is the rate of change of position, and acceleration is the rate of change of velocity. Distance and speed are scalar; displacement and velocity are directed quantities.

Use the right model

For uniform acceleration:

v=u+at,\quad s=ut+ rac12at^2,\quad v^2=u^2+2as

For projectiles without drag, solve horizontal and vertical components with a shared time. Do not use these equations when acceleration is non-uniform.

Check the boundary

Ask whether the quantity is average or instantaneous, whether the route or endpoints matter, whether acceleration is constant, and whether a neglected force such as drag changes the model.