a. A projectile is fired at an angle, θ, to the horizontal with velocity, u. Show that at any time, t, during the motion, the: i. horizontal component of the velocity is independent of t;
ii. vertical component of the velocity depends on t.
b. State the assumption on which projectile motion is based.
Explanation
i. From v = u + gt:
\(u_x\) = ucosθ, g = 0 (horizontal component is not affected by gravity)
\(v_x\) = ucosθ + (0)t
∴ \(v_x\) = ucosθ
ii. \(v_y = u_y + gt\)
∴ \(v_y = usinθ + gt\)
b. It assumes that the only force acting on the projectile is gravity, and there are no other forces, such as air resistance or drag, affecting its motion.