What's the fastest way?

The equation of motion of a projectile in the XY plane is y = 12 x 4 3 x 2 y=12x-\dfrac{4}{3}x^2 . Find the range of the projectile.


The answer is 9.

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2 solutions

Omkar Kulkarni
Aug 23, 2015

If you took the time of comparing this equation with y = x tan θ g x 2 2 u 2 cos 2 θ y=x\tan\theta-\dfrac{gx^2}{2u^2\cos^2\theta} or y = x tan θ ( 1 x R ) y=x\tan\theta\left(1-\dfrac{x}{R}\right) any other slower method, here's the solution.

At the end point, i.e., the point where the projectile meets the x-axis for the second time, the range is covered and the y-coordinate is zero. Hence substituting y = 0 y=0 , we get x = 9 x=9 .

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set y=0
12x - 4/3 x^2 = 0
4x( 3 - 1/3 x ) = 0
0,9 = x

RANGE = 9-0 = 9

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