The equation of motion of a projectile is $$y=12x$$−$$34x2$$ The horizontal component of velocity is $$3$$ $$ms-1$$. What is the range of the projectile?

Question

The equation of motion of a projectile is $$y=12x$$−$$34x2$$ The horizontal component of velocity is $$3$$ $$ms-1$$. What is the range of the projectile?

Infinity Learn · Accepted Answer

Given $$y=12x$$−$$34x2$$,$$ux=3ms$$−$$1$$ $$vy=dydt=12dxdt$$−$$32xdxdt$$  At $$x=0$$,$$vy=uy=12dxdt$$−$$12ux=12$$×$$3=36ms$$−$$1$$ $$ay=ddtdydt=12d2xdt2$$−$$32dxdt2+xd2xdt2$$  But $$d2xdt2=ax=0$$. Hence  $$ay=$$−$$32dxdt2=$$−$$32u2x=$$−$$32$$×$$(3)2=$$−$$272ms$$−$$2$$  Range, $$R=2uxuyay=2$$×$$3$$×$$3627/2=16m$$  Alternatively: We have $$y=12x$$−$$34x2$$.   When projectile again comes to ground, $$y=0$$ and $$x=R.0=12R$$−$$34R2$$⇒$$R=16m$$

The equation of motion of a projectile is $y = 12 x - \frac{3}{4} x^{2}$ The horizontal component of velocity is 3 ms^-1. What is the range of the projectile?

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The equation of motion of a projectile is y=12x−34x2 The horizontal component of velocity is 3 ms-1. What is the range of the projectile?

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The equation of motion of a projectile is $y = 12 x - \frac{3}{4} x^{2}$ The horizontal component of velocity is 3 ms^-1. What is the range of the projectile?