question_answer

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

A)  12.5 m/s                             

B)  25 m/s

C)  31.25 m/s          

D)         40 m/s

Correct Answer: D

Solution :

Let body be projected at an angle \[\theta \] with the horizontal at velocity u, then its time of flight is                 \[T=\frac{2u\,\,\sin \theta }{g}\]                                               ? (i) Also horizontal range\[R=u\cos \theta \times t\]                 \[R=\frac{u\cos \theta \times 2u\sin \theta }{g}\]                            ?. (ii) Given,   \[T=5\,\,s,\]      \[R=200\,\,m\] \[\therefore \]From Eqs. (i) and (ii), we get                 \[5=\frac{2u\,\,\sin \theta }{g}\]                                               ... (iii)           \[200=\frac{2{{u}^{2}}\sin \theta cos\theta }{g}\]                   ? (iv) Dividing Eq. (iv) by Eq. (iii), we get                 \[\frac{200}{5}=u\cos \theta =40\,\,m/s\]