Question

An arrow is shot into air. Its range is $200\, m$ and its time of flight is $5\, s$. If $g = 10\,ms^{- 2} $, then the horizontal component of velocity of the arrow is

• A. $ 12.5 \, ms^{ - 1} $
• B. $ 25 \, ms^{ - 1} $
• C. $ 31.25 \, ms^{ - 1} $
• D. $40 \, ms^{ - 1} $

Answer 1

Answer: (D)

$T = \frac{ 2 u \sin \theta }{ g } $ ..(i)
Also horizontal range $R = u \cos \, \theta \times t $
$R = \frac{ u \, \cos \, \theta \times 2 u \, \sin \, \theta }{ g }$ (ii)
Given $T = S$ and $R = 200$
$ \therefore $ From Eqs. (i) and (ii), we get
$5 = \frac{ 2 u \sin \, \theta }{ g } $ ..(iii)
$200 = \frac{ 2 u^2 \, \sin \, \theta \, \cos \, \theta }{ g } $ ..(iv)
Dividing Eq. (iv) by Eq. (iii), we get
$ \frac{ 200 }{ 5} = u \cos \theta = 40 \, ms^{ - 1} $