First slide

Projection Under uniform Acceleration

Question

A projectile is given an initial velocity of $\hat{i} + 2 \hat{j}$ The cartesian equation of its path is (g = 10 ms-²).

Moderate

A

$y = 2 x - 5 x^{2}$
B

$y = x - 5 x^{2}$
C

$4 y = 2 x - 5 x^{2}$
D

$y = 2 x - 25 x^{2}$

Solution

$\tan θ = \frac{u \sin θ}{u \cos θ} = \frac{2}{1} T h e d e s i r e d e q u a t i o n i s y = x \tan θ - \frac{g x^{2}}{2 u^{2} \cos^{2} θ} = x \times 2 - \frac{10 x^{2}}{2 {(\sqrt{2^{2} + 1^{2}})}^{2} {(\frac{1}{\sqrt{5}})}^{2} y = 2 x - 5 x^{2}}$

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