A projectile is fired horizontally from a gun that is 45.0 m above flat ground, it emerges from the gun with a speed of 500 m/s. (take, g = $- 10 m / s^{2}$ )

$C o l u m n - I C o l u m n - I I$
$(i) T i m e o f f l i g h t o f P r o j e c t i l e i n s (x) 3$
$(i i) H o r i z o n t a l d i s t a n c e c o v e r e d b y p r o j e c t i l e i n m (y) 30$
$(i i i) M a g n i t u d e o f v e r t i c a l c o m p o n e n t o f v e l o c i t y (z) 1500$
$i n m / s a s i t s t r i k e s g r o u n d$

(i) - (x); (ii) - (z); (iii) - (y)

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(i) - (y); (ii) - (x); (iii) - (z)

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(i) - (x); (ii) - (y); (iii) - (z)

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(i) - (z); (ii) - (x); (iii) - (y)

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Solution

The correct option is A
(i) - (x); (ii) - (z); (iii) - (y)

So the time for which the ball was in the air is the time that the ball took to fall 45 m in the y - direction.
Well that's fair to say,
So let's apply equation of motion.
$s$ = $u t + \frac{1}{2} a t^{2}$
$s_{y}$ = -45, $a_{y}$ = $- 10 m / s^{2}$
$u_{y}$ = $0$ $\Rightarrow$ ${- 45}^{9}$ = $- \frac{1}{2} \times 10^{2} \times t^{2}$
$t$ = $3 s e c$
so the ball was in air for 3 sec
time of flight = 3 sec
now we need to find the horizontal distance covered by the ball.
So let's see what we know about the motion in x
$u_{x}$ = 500 m/s
$a_{x}$ = 0 No acceleration in x-direction
The ball was in air for 3 sec
$\Rightarrow$ t = 3
$s_{x}$ = $u_{x} t$
= $500 \times 3$
$s_{x}$ = $1500 m$
Next part of the equation asks the vertical compound of velocity when the ball hits the ground.
So I need to focus on the motion in y-direction only and should not care about x-direction as they both are independent of each other
So I know
$u_{y}$ = $0$
$a_{y}$ = $- 10 m / s^{2}$
$s_{y}$ = $- 45 m$
$t$ = $3 s e c$
what I need is $V_{y}$ -equation of motion
$v$ = $u + a t$
Simple
$v_{y}$ = $- 10 \times 3$
$v_{y}$ = $- 30 m / s$
So the vertical copmponent of the ball when it hits the ground is $30 m / s$ in the negative y-direction.

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A projectile is fired horizontally from a gun that is 45.0 m above flat ground, it emerges from the gun with a speed of 500 m/s. (take, g = $- 10 m / s^{2}$ )

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