(1) Derive equation of trajectory for horizontal projectile. 1 (2) derive the expression for time of flight & horizontal range for given parabola. 2 (3) Derive the equation for regultant velocity at any instant & also give its direction.

Asked by  | 22nd Oct, 2013, 01:42: PM

Expert Answer:

1) The path of the projectile is shown below
 
 
The horizontal component of velocity always remain same as there is no acceleration on the horizontal axis.
 
Thus, the horizontal distance travelled by the projectile is
 
x = u cos? × t
 
t = x/(u cos?)                                                   ...... (1)
 
The vertical distance travelled by projectile is given from kinematical equation s = ut + ½at2.
Here, s = y, a = ay = -g, u = uy = u sin?
 
Thus, we have
 
y = u sin? - ½gt2                                              ...... (2)
 
Substituting equation (1) in (2), we get
 
 
This is the equation of trajectory of the projectile.
 
 
Kindly ask separate questions as separate queries.

Answered by Romal Bhansali | 24th Oct, 2013, 09:24: AM

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