Question

A projectile is fired with a velocity u making an angle θ with the horizontal. Show that its trajectory is a parabola. Derive expressions for (i) maximum height (ii) Time of flight.

Answer 1

A projectile is fired with a velocity u making an angle θ with the horizontal.

Now, we can say:

In X axis :

$x = u \cos( \theta) \times t$

In Y axis :

$y = u \sin( \theta) t - \dfrac{1}{2} g {t}^{2}$

Now, putting value of t in eq.(2):

$y = \bigg \{ u \sin( \theta) \times \dfrac{x}{u \cos( \theta) } \bigg \} - \dfrac{1}{2} g { \bigg \{\dfrac{x}{u \cos( \theta) } \bigg \}}^{2}$

$\boxed{\implies y = x \tan( \theta) - \dfrac{g {x}^{2} }{2 {u}^{2} { \cos}^{2}( \theta) }}$

This equation is very similar to:

$\boxed{y = ax - bx^{2}}$

Hence, the equation is that of a parabola.

Regarding Range and Time period, please click the below link:

https://brainly.in/question/12502855