Projectile motion: Qualitative treatment of lift and drag forces.

The idea

Lift and drag are contact forces exerted by a fluid on a body moving through it. Drag acts opposite to the relative motion of the fluid and increases with speed, cross-sectional area and fluid density; it also depends on shape. Lift acts perpendicular to the relative flow and arises when a shape deflects fluid, so a wing generates upward lift as air is pushed downward. In projectile motion, drag reduces both the horizontal and vertical velocity components, so the path becomes asymmetric and the range and maximum height fall. Lift can matter for spinning or aerofoil-shaped projectiles. A useful method is to draw the velocity vector, then draw drag antiparallel to it and lift at 90° to it, before resolving.

What earns the marks

• Drag is a fluid resistance force acting in the direction opposite to the body's velocity relative to the fluid.
• Drag magnitude increases with speed, frontal area and fluid density, and depends on the object's shape.
• Lift acts perpendicular to the relative flow direction and is produced when a shape deflects the fluid.
• For a projectile, drag removes energy and reduces both velocity components, lowering range and maximum height.
• Lift can change the vertical motion of a spinning or aerofoil-shaped projectile, so the trajectory is not a simple parabola.
• A valid qualitative explanation links force directions to the resulting change in the velocity vector.

Common mistakes and how to put them right

• Treating drag as always vertically upward.

  Put it right by stating that drag is antiparallel to the relative velocity, so it tilts as the projectile moves.

• Confusing lift with the upward normal force from a solid surface.

  Put it right by defining lift as a fluid force perpendicular to the relative flow.

• Assuming drag is constant during flight.

  Put it right by explaining that drag falls as the projectile slows, so the deceleration is not uniform.

Exam tips

• Sketch the velocity vector first, then add drag opposite it and lift at 90° to it before writing any explanation.
• Use comparative language such as greater speed gives greater drag, and link each force to the change it causes in the velocity components.
• When asked about projectile motion with drag, state that the path is asymmetric and that range and maximum height are reduced compared with ideal projectile motion.