Question

need solution with explanation plz​

Answer 1

$\huge{\bold{\underline{\underline{....Answer....}}}}$

$\huge{\bold{\underline{Given:-}}}$

$\large{\bold{X = 36t}}$

$\large{\bold{2y = 96t - 9.8 t^2}}$

$\huge{\bold{\underline{Explanation:-}}}$

Simplifying,

$\large{\bold{y = 48t - 4.9t^2}}$

Taking the x coordinate,

$\large{x = 36t}$

Now,

$\large{t = \dfrac{x}{36} \: -----(1)}$

Substituting the equation (1) in y - coordinate,

$\large{y = 48t - 9.8 t^2}$

$\large{y = 48 \times \dfrac{x}{36} - 4.9 \times \left[ \dfrac{x}{36} \right]^2}$

Simplifying,

$\large{y = \dfrac{4}{3} .x - 4.9 \times \left[ \dfrac{x}{36} \right]^2}$

Comparing with equation of trajectory,

$\large{\bold{y = (\tan \theta)x - \left[ \dfrac{g}{2u^2 \cos^2 \theta} \right] x^2}}$

We get,

$\large{\boxed{ \tan \theta = \dfrac{4}{3}}}$

But the given options are in sine angle then,

#refer the attachment for figure.

As we know 3, 4, 5 are pythagorean triplets.

Therefore,

Hypotenuse (AC) will be 5.

Now,

$\large{ \sin \theta = \dfrac{AB}{AC}}$

Substituting the values,

$\large{ \sin \theta = \dfrac{4}{5}}$

$\huge{\boxed{\boxed{ \theta = sin^{-1} \left[ \dfrac{4}{5} \right]}}}$

So, the correct Option is (A).