CBSE Class 11-science Answered
Show that for a projection angle θ, where 0° < θ <90°, the path of the projectile is a parabola.
Asked by debjit_dm | 24 Apr, 2020, 03:04: PM
Expert Answer
Let us assume y-axis is verical direction and x-axis horizontal direction.
Let Projectile be projected from origin of x-y coordinate system.
Y-coordinate of projectile at tme t , y = ( u sinα ) t - (1/2) g t2 ............ (1)
where u is projection velocity, α is angle of projectin and g is acceleration due to gravity
X-coordinate of projectile at time t , x = ( u cosα ) t ...................(2)
Let us eliminate time t from above equation by using the substitution for time t from eqn.(2)
y = ( u sinα ) [ x / ( u cosα ) ]- (1/2) g [ x / ( u cosα ) ]2
y = ( tanα ) x - [ g / ( 2 u2 cos2α ) ] x2 .............................. (3)
Above relation is the trajectory of projectile, which is second degree equation in terms of x-ccordinate.
Hence trajectory of projectile is parabola
Answered by Thiyagarajan K | 24 Apr, 2020, 03:47: PM
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