Question

How to resolve velocity vector of a projectile motion into horizontal and vertical components?And how to find the time of flight using the components?

Answer 1

Firstly,understand the following concepts,

• projectile is any object upon which the only force is gravity,
• Projectiles travel with a parabolic trajectory due to the influence of gravity,
• There are no horizontal forces acting upon projectiles and thus no horizontal acceleration,
• The horizontal velocity of a projectile is constant (a never changing in value),
• There is a vertical acceleration caused by gravity; its value is 9.8 m/s/s, down,
• The vertical velocity of a projectile changes by 9.8 m/s each second,
• The horizontal motion of a projectile is independent of its vertical motion.
• Therefore only vertical component is used in the calculation of time of flight of projectiles.

• To find the time of flight, determine the time the projectile takes to reach maximum height. The time of flight is just double the maximum-height time.

  Start with the equation:

  v_y = v_oy + a_y t

  At maximum height, v_y = 0.

  The time to reach maximum height is t_1/2 = - v_oy / a_y

  Time of flight is t = 2t_1/2 = - 2v_oy / a_y

  Plugging in v_oy = v_o sin(q) and a_y = -g, gives:

  Time of flight is t = 2 v_o sin(q) / g

  where g = 9.8 m/s²

  The time of flight is also determined solely by the initial velocity in the y direction and the acceleration due to gravity.
  
  Read it carefully and try to understand it. Everything is explained in detail.Hope you understood.