The path of the projectile is parabolic and show by proofing it?
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a) horizontal direction
s = ut + 1/2at²
x = u(x)t + 1/2.0.t² (a= 0)
x = ucosø.t
t = x/ucosø...........(1)
b) vertical direction
s = ut + 1/2 at²
y = u(y)t + 1/2a(y).t [a(y) = -g]
y = usinø.t - 1/2.g.t²
y = usinø.t - 1/2.g.t²
Put t = x/ucosø from equation 1
y = usinø.x/ucosø - 1/2.g.(x/ucosø)²
y = xtanø - 1/2.gx²/u²cos²ø
y = xtanø - (gsec²ø/2u²).x²
Let a = tanø and b = -gsec²ø/2u²
y = ax + bx²
y is proportional to x², which is an equation of parabola.
Therefore, the path followed by projectile is a parabola.
s = ut + 1/2at²
x = u(x)t + 1/2.0.t² (a= 0)
x = ucosø.t
t = x/ucosø...........(1)
b) vertical direction
s = ut + 1/2 at²
y = u(y)t + 1/2a(y).t [a(y) = -g]
y = usinø.t - 1/2.g.t²
y = usinø.t - 1/2.g.t²
Put t = x/ucosø from equation 1
y = usinø.x/ucosø - 1/2.g.(x/ucosø)²
y = xtanø - 1/2.gx²/u²cos²ø
y = xtanø - (gsec²ø/2u²).x²
Let a = tanø and b = -gsec²ø/2u²
y = ax + bx²
y is proportional to x², which is an equation of parabola.
Therefore, the path followed by projectile is a parabola.
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