A ball 'A' is projected from origin with an initial velocity `v_(0)` = 700 cm/sec in a direction `37^(@)` above the horizontal as shown in fig .Another ball 'B' 300 cm from origin on a line `37^(@)` above the horizontal is released from rest at the instant A starts. How far will B have fallen when it is hit by A ?

Options

A. 90 cm
B. 80 cm
C. 70 cm
D. 60 cm

Answer

A

Explanation

From `DeltaBOC,"sin" 37^(@) = (BC)/(OB)`
`BC=300 "sin" 37^(@) =300 xx 3/5 =180 cm`
Let bal A and ball B collide after a time t `:.` for ball A, along vertical
`s_(y) =u_(y) +1/2 a_(y) t^(2)`
`= 700 "sin" 37^(@) t+1/2(-g) r^(2)`
`AC =420 t- ("gt"^(2))/(2)`
For ball B height fallen along vertical
`s="ut"+1/2 a t^(2) rArr -BA =(0) t+1/2(-g) r^(2)`
`BA =("gt"^(2))/(2)`
`BA+AC =BC =180`
`("gt"^(2))/(2) +420t - ("gt"^(2))/(2) =180`
`420 t=180`
`t =(180)/(420) =3/7 "sec"`
`:. BA =("gt"^(2))/(2) =(980)/(2)xx(9)/(49)=90 "cm"`