Question

A ball is thrown with a velocity of 100m/s at an angle of 30degrees to the horizontal and meets the same horizontal plane later.find
(a)it's time of flight
(b)the horizontal it travels
(c)the velocity with which it strikes the ground at the end of it's flight [g=9.8]dfh

Answer 1

$time \: of \: flight = \frac{2u \sin(30) }{g} \\ = \frac{2 \times 100 \times \frac{1}{2} }{10} \\ = 10 \: seconds$
$horizontal \: range = \frac{2 {u}^{2} \sin(30) \cos(30) ) }{g} \\ = \frac{2 \times 100 \times 100\times \frac{1}{2} \times \frac{ \sqrt{3} }{2} }{10} \\ = 500 \sqrt{3} m$
Final velocity = Initial velocity = 100m/s

Answer 2

Given:

Initial velocity $\left( { v }_{ 0 } \right)$ = 100 m/s

Angle of the stone = 30°

Solution:

(a) Time of flight = ?

$Time\quad of\quad flight\quad =\quad \frac { 2{ v }_{ 0 }\sin { \theta } }{ g }$

Where,

${ v }_{ 0 }$ = Initial velocity

g = Acceleration due to gravity

$\Rightarrow \quad Time\quad of\quad flight\quad =\quad \frac { 2\quad \times \quad 100\quad \times \quad \sin { 30° } }{ 9.8 }$

$\therefore \quad Time\quad of\quad flight\quad =\quad 10.20\quad s$

(b) Horizontal range = ?

$Horizontal\quad range\quad =\quad R\quad =\quad \frac { { v }_{ 0 }^{ 2 }\sin { 2\theta } }{ g }$

$\Rightarrow \quad R\quad =\quad \frac { { 100 }^{ 2 }\quad \times \quad \sin { 2\left( 30° \right) } }{ 9.8 }$

$=\quad \frac { { 100 }^{ 2 }\quad \times \quad \sin { \left( 60° \right) } }{ 9.8 }$

$\Rightarrow \quad R\quad =\quad 883.6\quad m$

(c) Final velocity = ?

$Final\quad velocity\quad =\quad v\quad =\quad \frac { 2\left( x\quad -\quad { x }_{ 0 } \right) }{ t } \quad -\quad { v }_{ 0 }$

$=\quad \frac { 2\left( 883.6 \right) }{ 10.20 } \quad -\quad 100$

$\Rightarrow \quad Final\quad velocity\quad =\quad 73.27\quad m/s$

The velocity with which it strikes the ground = 73.27 m/s