Projectile Motion

Projectile Motion Overview

  • Definition: A projectile is an object that is dropped or launched into the air.

  • Examples of Projectile Motion:

    • Horizontal Projectile Motion: No initial vertical velocity.

    • Projectile Motion at an Angle: Launched from an angled position.

    • Projectile Motion from Non-Zero Position: Starts or ends from a height.

  • Important Note: Separate vertical and horizontal components when solving projectile motion questions.

  • Equations of Motion: Utilize relevant equations to solve projectile motion problems.

Vertical Projectile Motion

Going Up

  • The only force acting is gravity (downward).

  • Gravity acts as a deceleration: ( a = -9.8 \text{ m/s}^2 )

  • At the top, the object’s velocity is zero: ( v = 0 \text{ m/s} )

Going Down

  • The only force acting is again gravity (downward).

  • Gravity acts as an acceleration: ( a = 9.8 \text{ m/s}^2 )

  • Starts from rest: ( v = 0 \text{ m/s} )

Example Problems in Vertical Projectile Motion

  • Camera Drop: A camera dropped from a height. Sound heard 3.0 seconds later.

    • Calculate how far it fell and the velocity upon hitting the ground.

  • Dancer's Jump: A dancer jumps with an initial velocity of 4.0 m/s from 1.0 m above ground.

    • Determine time to max height, max displacement, acceleration at the peak, and return velocity.

Projectile Motion Components

Vertical Components

  • Equations to note:

    • uy=u/sin(θ)

Horizontal Components

  • Equations:

    • s=ut

    • ux=u/cos(θ)

Projectiles Launched Obliquely

Vertical Component Behavior

  • Upward movement: ( a = -9.8 \text{ m/s}^2 )

  • Downward movement: ( a = 9.8 \text{ m/s}^2 )

Horizontal Component Behavior

  • No forces act horizontally (ignoring air resistance), so velocity remains constant and acceleration is zero.

Range Equation

  • Caution: Selecting variables correctly is tedious but essential.

  • Range Equation Condition: Trajectory must be symmetrical (start and finish at the same height).

Example Problems with Calculations

  • Golf Ball Case: Golf ball hit from 30.0 m high cliff.

    • Calculate time to land, horizontal travel distance (range), and velocity at impact.

  • Ball Thrown Horizontally: Ball thrown from height of 2.0 m, taking 4.0 seconds to land.

    • Determine height of cliff, horizontal distance, vertical impact speed, and angle.

  • Hockey Ball Case: Hockey ball hit at 25° with speed of 32 km/h.

    • Assess horizontal and vertical velocity components, flight duration, and range.

  • A stunt driver jumps a car over a river (50 m wide) at 40° at 22 m/s.

    • Assess if the car makes the jump based on calculations.

Effects of Air Resistance

Comparison of Motions

  • When an object travels upward, gravity decelerates it (also impacts its travel downward).

Object Drop Scenario

  • Comparison: Elephant vs. 50-cent coin drop.

    • With no air resistance, they hit the ground simultaneously.

Impact of Air Resistance on Motion

  • Always opposes projectile motion direction. Affects:

    • Maximum height (reduced)

    • Maximum range (shortened)