Two particles A and B projected simultaneously from a point situated on a horizontal place. The particle A is projected vertically up with a velcity `v_(A)` while the particle B is projected up at an angle `30^(@)` with horizontal with velocity `v_(B)`. After 5s the particles were observed moving mutually perpendicular to each other. The velocity of projection of the particle `v_(A) and v_(B)` respectively are:

Options

A. `50ms^(-1), 100m//s`
B. `100ms^(-1), 50m//s`
C. `v_(A)` can have any value greater than a certain value, `100ms^(-1)`
D. none of these

Answer

c

Explanation

Velocity of A is always in vertical direction. At 5s, velocity of B is perpendicular to that of A. It means velocity of B is horizontal or B is at highest point.
Time of ascent `=(v_(B)sin 30^(@))/g=5s`
Now velocity of A can have any value provided its time of flight is more than 5s.
For this `v_(A)ge25m//s`