Find the time in the following:

Question

A projectile is fired from ground with a speed of 20m/s at an angle of 30 degrees with the horizontal. At what time, the velocity vector of projectile becomes perpendicular to initial velocity.

Answer 1

The velocity vector of the projectile body initially is 

v0=ucos30i+usin30j, 

after a time t the velocity vector is 

v=ucos30i+(usin30-gt)j 

The two vectors are perpendicular so their dot product is zero. we get that ucos30xucos30+usin30xusin30=ugtsin30

=>u²=ugtsin30

=>t=u/gsin30

=> t=2u/g

=> t = 2*20/10 (g = 10)

=> t = 4 sec