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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
answered-by-expert 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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