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

The Correct Option is D

T = $ \frac{ 2 u \sin \theta }{ g } $ $ \hspace20mm $ ..(i) Also horizontal range R = $ u \cos \, \theta \times t $ R = $ \frac{ u \, \cos \, \theta \times 2 u \, \sin \, \theta }{ g } $ $ \hspace20mm $ ..(ii) Given T = S and R = 200 $ \therefore $ From Eqs. (i) and (ii), we get 5 = $ \frac{ 2 u \sin \, \theta }{ g } $ $ \hspace20mm $ ..(iii) 200 = $ \frac{ 2 u^2 \, \sin \, \theta \, \cos \, \theta }{ g } $ $ \hspace20mm $ ..(iv) Dividing E (iv) by E (iii), we get $ \frac{ 200 }{ 5} = u \cos \theta = 40 \, ms^{ - 1} $