a spotlight S rotates in a horizontal plane with a constant angular vel. of o.1 rad/s . The spot of light P moves alsong the wall at a distance of 3 m .What is The vel. of the spot P when angle is 45?
Q2 . on frictionless horizontal surface , assumed to be the x-y plane , a small trolley is movin along a st. line parallel to the y axis with a const. vel. of (root 3 - 1 ) m/s . At a particular instant , when the line OA makes an angle of 45 degrees with the X axis , a ball is thrown along the surface frm the origin O . its vel makes an angle q with the x axis and it hits the trolley . FIND the speed of the ball wrt the surface , if q = 4 theta / 3.
1If i m nt wrong then \theta is the angle made by the velocity vectorof the ball with the x-axisin that frame...
then clearly \theta=45° (rel. vel of ball wrt trolley must be along OA to hit the trolley)
hence \phi = 4\theta /3 = 60°
let v be the vel of ball
vx= v/2 and vy=√3v/2
now (vel of ball wrt trolley)x = v/2 (vtrolley x=0)
(vel of ball wrt trolley)y = √3v/2 - (√3-1)
tan\theta=√3v/2 - (√3-1)v/2
which gives v=2m/s
6hmmm
ya e1 i mgettin that
but the book in which i saw it had given the ans as 0.6
it must be wrong!!
