Question

Show that path of projectile is parabola?

Answer 1

Let a body is projected with speed u m/s inclined θ with horizontal line .
Then, vertical component of u, = ucosθ
Horizontal component of u , = usinθ
acceleration on horizontal, ax = 0
acceleration on vertical, ay = -g


Now, use formula,
x = ucosθ.t
t = x/ucosθ------(1)

Again, y = usinθt - 1/2gt²
Put equation (1) here,
y = usinθ × x/ucosθ - 1/2g × x²/u²cos²θ
y = tanθx - 1/2gx²/u²cos²θ

This equation is similar to Standard equation of parabola y = ax² + bx + c her, a, b and c are constant

So, A projectile motion is a parabolic motion.