The equation of motion of a projectile is : y = 12x- $\frac{3}{4} x^{2}$
The horizontal component of velocity is 3 ${ms}^{- 1}$ . Given that g = 10 ${ms}^{- 2}$ , what is the range of the projectile?

Question

The equation of motion of a projectile is :  y  $$=$$ $$12x-34x2The$$ horizontal component of velocity is $$3$$ $$ms-1$$. Given that g $$=$$ $$10$$ $$ms-2$$, what is the range of the projectile?

Infinity Learn · Accepted Answer

y $$=$$ $$12x$$ $$-$$ $$34x2dydt$$ $$=$$ $$12dxdt-32xdxdtAt$$ x $$=$$ $$0$$, dydt $$=12dxdt$$ If θ be the angle of projection, thendydtdxdt $$=$$ $$12$$ $$=$$ $$tan$$ θAlso, if u $$=$$ initial velocity, then u $$cos$$ θ $$=$$ $$3Hence$$, $$tan$$ θ × $$cos$$ θ $$=$$ $$36$$ or u $$sin$$ θ $$=$$ $$36Range$$ R $$=$$ $$u2$$ $$sin$$ $$2$$θg $$=$$ $$2u2sin$$ θ $$cos$$ θg              $$=$$ $$2(u$$ $$sin$$ θ$$)(u$$ $$cos$$ θ$$)10$$ $$=$$ $$2$$×$$36$$×$$310$$ $$=$$ $$21.6$$ m

The equation of motion of a projectile is : y = 12x- $\frac{3}{4} x^{2}$
The horizontal component of velocity is 3 ${ms}^{- 1}$ . Given that g = 10 ${ms}^{- 2}$ , what is the range of the projectile?

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The equation of motion of a projectile is : y = 12x-34x2The horizontal component of velocity is 3 ms-1. Given that g = 10 ms-2, what is the range of the projectile?

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The equation of motion of a projectile is : y = 12x- $\frac{3}{4} x^{2}$
The horizontal component of velocity is 3 ${ms}^{- 1}$ . Given that g = 10 ${ms}^{- 2}$ , what is the range of the projectile?