science projevtion

• Projectile motion


  Combination of horizontal motion with constant velocity and vertical motion with constant acceleration
• Horizontal component of projectile motion


  • Acceleration equal to zero (ax=0) since the horizontal component of the velocity of projectiles is constant
• Vertical component of acceleration


  • Constant, equal to the acceleration due to gravity (ay= -g)
• Equations of motion with respect to x and y-axis


  x = x0 + v0xt

  y = y0 + v0yt - 1/2 gt^2
• Equations for velocities


  vx = v0x

  vy = v0y - gt
• Factors affecting height and range of a projectile


  • Initial velocity (v0)

  1. Angle of launch (θ)
• Equations for x and y components of initial velocity


  v0x = v0 cos θ

  v0y = v0 sin θ
• Equations of motion for final position

  x = x0 + v0x t

  y = y0 + v0y t - 1/2 gt^2
• Conditions for projectile motion: Object thrown with initial velocity v0 at angle of launch θ
• Trajectory of projectile


  • Parabolic
• At peak of parabola, vertical component of velocity is zero (vy=0)
• Time when projectile reaches maximum height


  t = v0y/g
• Maximum height (H)


  H = v0y^2 / 2g
• Time to go down to same level (tdown) = time to go up (tup)
• Total time of flight (T)

  T = 2t
• Equation for maximum range (R)


  R = (v0^2 * sin(2θ)) / g
• Range and height depend on angle of launch (θ)
• Salient values of angle θ


  • θ = 0°: Horizontal motion only, height = 0

  θ = 90°: Vertical motion only, range = 0

  1° < θ < 89°: Projectile motion evident
• When θ = 45°, horizontal displacement is maximum with high vertical displacement
• When θ = 89°, vertical displacement is maximum with low horizontal displacement