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Question

Physics Question on Motion in a plane

An arrow is shot into air. Its range is 200 m and its time of flight is 5 s. If g = 10 ms2ms^{- 2}, then the horizontal component of velocity of the arrow is

A

12.5ms112.5 \, ms^{ - 1}

B

25ms125 \, ms^{ - 1}

C

31.25ms131.25 \, ms^{ - 1}

D

40ms140 \, ms^{ - 1}

Answer

40ms140 \, ms^{ - 1}

Explanation

Solution

T = 2usinθg\frac{ 2 u \sin \theta }{ g } \hspace20mm ..(i) Also horizontal range R = ucosθ×tu \cos \, \theta \times t R = ucosθ×2usinθg\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 = 2usinθg\frac{ 2 u \sin \, \theta }{ g } \hspace20mm ..(iii) 200 = 2u2sinθcosθg\frac{ 2 u^2 \, \sin \, \theta \, \cos \, \theta }{ g } \hspace20mm ..(iv) Dividing E (iv) by E (iii), we get 2005=ucosθ=40ms1\frac{ 200 }{ 5} = u \cos \theta = 40 \, ms^{ - 1}