A train is moving with a constant speed of `10m//s` in a circle of radius `16/pi`m. The plane of the circle lies in horizontal x-y plane. At time t = 0, train is at point P and moving in counter- clockwise direction. At this instant, a stone is thrown from the train with speed `10m//s` relative to train towards negative x-axis at an angle of `37^@` with vertical z-axis . Find
(a) the velocity of particle relative to train at the highest point of its
trajectory.
(b) the co-ordinates of points on the ground where it finally falls and that of the hightest point of its trajectory. (Take g `= 10 m//s^2, sin 37^@ = 3/5`

Options

A. `(pi)/2`
B. `(pi)/4`
C. `pi`
D. `(3pi)/4`

Answer

A

Explanation

At `t=0`
`vecv_T=10hatjm//s`
`vecv_(s/T)=-6hati+8hatkm//s`
`vecv_S=vecv_(ST)=vecv_T=(-6hati+10hatj+8hatk)m//s`
Time of flight of the stone`=TG=(2v_g)/g=8/5s`
For the highest point `t_a=T//2=4//5s`
Angular displacement of train in time `t_a=omegat_a`
`=(v/r)t_a=(10/(16//pi))(4//5)=(pi)/2`
At the highest point `vecv_S=-6hati+10hatj`
`vecv_S=-10hati, vecv_(ST)=vecv_S-vecv_T=4hati=10hatj`
`vecS=vecv_("horizontal")T=[-6hati+10hatj]1.6=-9.6hati+16hatj`