Projectile motion: Factors affecting horizontal displacement of projectiles.

The idea

Horizontal displacement of a projectile is the horizontal distance it travels from release or projection to landing. It depends on the horizontal velocity at release, the time the projectile spends in the air, and the angle of release. For a projectile released and landing at the same height, horizontal displacement equals horizontal velocity × flight time. Flight time is determined by the vertical component of velocity and gravity: a larger vertical component or a greater release height increases time in the air. The angle of release affects how the initial velocity splits into horizontal and vertical components. In many sporting situations, such as a shot put or long jump, the optimum angle is less than 45° because release height and the need for horizontal speed reduce the ideal angle.

What earns the marks

• Horizontal displacement is the horizontal distance a projectile travels from release to landing.
• Horizontal displacement equals horizontal velocity multiplied by flight time.
• Horizontal velocity at release affects how far the projectile travels horizontally in a given time.
• Flight time depends on the vertical component of velocity, gravity and release height.
• The angle of release determines the split of initial velocity into horizontal and vertical components.
• In sport, the optimum angle of release is often less than 45° because of release height and the need to maximise horizontal velocity.

Common mistakes and how to put them right

• Thinking horizontal velocity changes during flight.

  Put it right: In the absence of air resistance, horizontal velocity remains constant, so horizontal displacement depends on that constant velocity and the time in the air.

• Assuming 45° is always the best angle of release.

  Put it right: When release height is above landing height, or when horizontal speed is important, the optimum angle is often less than 45°.

• Confusing horizontal and vertical components.

  Put it right: The vertical component affects flight time, while the horizontal component affects how far the projectile travels horizontally.

• Believing gravity acts horizontally.

  Put it right: Gravity acts vertically downwards, so it changes vertical velocity but not horizontal velocity.

Exam tips

• Identify the horizontal velocity and the flight time before calculating or explaining horizontal displacement.
• Explain how release angle changes the horizontal and vertical components of the initial velocity.
• Use sporting examples such as shot put or long jump to show why the optimum angle may be less than 45°.