Question

Q1.A projectile can have same range R for angle x and (90°-x) if t1 and t2 are time of flight then what is the relation between R,t1 and t2 ?

Answer 1

Step-by-step explanation:

The horizontal range of a projectile is given by,

$R = \frac{ {u}^{2}sin(2x) }{g}$

Since

⇒sin2( 90 - x )= sin( 180-x ) = sinx

Therefore, Range of projectile is same for two angles x and 90 - x.

The Time of flight of a projectile is given by,

$T= \frac{2u \sin( \theta) }{g}$

Given t₁, t₂ are time of flights respectively then,

$\begin{gathered}t _{1} = \frac{2u \sin( x) }{g} \\ \\ t _{2} = \frac{2u \sin( 90 - x) }{g} = \frac{2u \cos( x) }{g} \end{gathered}$

Let us consider,

$R =x t_{1} t_{2}$

Now,

$\begin{gathered} \frac{ {u}^{2}sin(2x) }{g} = \: x \frac{2u \sin( x) }{g} \times \frac{2u \cos( x) }{g} \\ \\ \sin(2x) = x \times 2 \sin(2x) \times \frac{1}{g} \\ \\ x = \frac{g}{2} \end{gathered}$

Therefore, R = 1/2gt₁t₂

Answer 2

Answer:

Michelangelo di Lodovico Buonarroti Simoni, known simply as Michelangelo, was an Italian sculptor, painter, architect and poet of the High Renaissance born in the Republic of Florence, who exerted an unparalleled influence on the development of Western art.