Show that the path of the projectile is a parabola in case of horizontal projection.
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11th
Physics
Motion in a Plane
Projectile Motion
Show that the path of a pro...
PHYSICS
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Asked on December 26, 2019 by
Gurpreet Sree
Show that the path of a projectile is a parabola
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Let a body is projected with speed um/s inclined θ with horizontal line.
Then, vertical component of u, u
y
=ucosθ
Horizontal component of u
x
=usinθ
acceleration on horizontal, ax=0
acceleration on vertical, ay=−g
Now, use formula
X=u
x
t
X=ucosθ.t
t=X/ucosθ--------------------------(1)
Again, y=u
y
t+1/2a
y
t
2
y=usinθt−1/2gt
2
put equation (1) here,
y=usinθ×x/ucosθ−1/2gt
2
×x
2
/u
2
cos
2
θ
=tanθx−1/2gx
2
/u
2
cos
2
y=tanθ.x−1/2gx
2
/u
2
cos
2
θ
this equation is similar to standard equation of parabola y=ax
2
+bx+c her, a,band c are constant
So, A projectile motion is parabolic motion.