Asked by Venkat phy lect | 6th Jul, 2013, 08:21: PM

Expert Answer:

You can easily prove that by using the 3 laws of motion. 
Let the projectile have an initial velocity u at an angle ? with the horizontal.

As no external force acts on the projectile in the horizontal direction, the horizontal component of the velocity is constant.
=> horizontal displacement, x, in time t is
x = u cos? * t ... (1)

In the vertical direction, there is an acceleration due to gravity in the downward direction.
=> vertically upward displacement, y, in time t is
y = u sin? * t - (g/2) * t^2 ... (2)

Eliminating t from both the equations,
y = x tan? - (g/2) * (x^2/u^2cos^2 ?)

This equation is of the form,
y = ax - bx^2,
where a = tan? and b = g / (2u^2 cos^2 ?) are constants.

Answered by  | 7th Jul, 2013, 12:23: AM

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