Question

$\mathfrak{\underline{\underline{Hey Brainliacs}}$

Solve this question:

Explain angular projection and derive all its components
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Answer 1

Answer:

★ Angular projection : The projectile motion of an object in ehich the initial velocity and fall under influence of gravity.

⚕Equation of trajectory :

➣Formula to be used here :

$\boxed{\sf{s = ut+ \dfrac{1}{2} at^2}}$

❇ Equation of motion along x axis:

➫$\sf{s_x = u_x t + \dfrac{1}{2}a_x t^2}$

➫$\sf{x = (ucos \theta) t + \dfrac{1}{2} \times 0 \times t}$

➫$\sf{x = u cos \theta \ t}$

➫$\sf{ = \dfrac{x}{u cos\theta}}$ - (i)

❇ Equation of motion along y axis:

➫$\sf{s_y = u_y t +\dfrac{1}{2}a_y t^2}$

➫$\sf{s_y = (u sin \theta) t + \dfrac{1}{2} \times -g \times t^2}$

Putting value of t from (i) :

→$\sf{y = (usin\theta)\dfrac{x}{u cos \theta} - \dfrac{-g}{2} \dfrac{x^2}{u^2 cos^2 \theta}}$

→$\sf{y = x tan \theta - \dfrac{gx^2}{2u^2 cos^2 \theta}}$

⚕Time of flight :

➣Formula to be used here :

$\boxed{\sf{v = u + at}}$

❇ Time of flight at highest point :

➫$\sf{v_y = u sin \theta + (-g)t}$

➫$\sf{0 = u sin \theta - gt}$

➫$\sf{t = \dfrac{u sin \theta}{g}}$

✦$\sf{Time \ of \ flight = \dfrac{2u sin \theta}{g}}$

⚕Maximum height :

➣Formula to be used here;

$\boxed{\sf{v^2 - u^2 = 2as}}$

❇ Using equation:

➫$\sf{v_y^2 - u_y^2 = 2a_y s_y}$

➫$\sf{0 - \dfrac{u^2 sin^2 \theta} = 2gh}$

➫$\sf{H = \dfrac{u^2 sin^2 \theta}{2g}}$

⚕Horizontal Range:

❇ Using equation of distance:

➫$\sf{s_x = u_x t + \dfrac{1}{2}a_x t^2}$

➫$\sf{x = (u cos \theta )t + 0}$

➫$\sf{R =( u cos\theta )T}$

➫$\sf{R = u cos \theta \times \dfrac{2 u sin \theta}{g}}$

➫$\sf{R = \dfrac{u^2 sin 2\theta}{g}}$

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