2020HSCShort answer

Q12 (b) (ii)

3 marks

Question

Using the projectile model from part (i), show that the Cartesian equation of the path of flight is
$y=\frac{-gx^2}{2u^2}\left(\tan^2\theta-\frac{2u^2}{gx}\tan\theta+1\right).$

Try the question before revealing the answer.

Solution

Criteria	Marks
Provides correct solution	3
Obtains a correct Cartesian equation of flight, or equivalent merit	2
Attempts to eliminate $t$ , or equivalent merit	1

Sample answer:

x=ut\cos\theta\Rightarrow t=\frac{x}{u\cos\theta}

y=ut\sin\theta-\frac12gt^2

= x\tan\theta-\frac{gx^2}{2u^2}(1+\tan^2\theta)

=-\frac{gx^2}{2u^2}\left(\tan^2\theta-\frac{2u^2}{gx}\tan\theta+1\right)

Supplied marking guidance · human reviewed

Compare this with your working, not only your final sentence.

Syllabus alignment

Mechanics

Projectiles and resisted motionUse parametric and Cartesian equations to solve projectile problems with and without resistance.

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