A particle is projected horizontal with a speed of 20/√3m/s from some height at t=0. at what time will its velocity make 60degree angle with the initial velocity?

1 Answer
P dilip_k
Jun 23, 2017

drawn

A particle is projected horizontal and the initial horizontal component of the velocity of the projected particle
#V_h =20/sqrt3#, This will remain unchanged during its flight.

The initial vertical component of the velocity of the projected particle #V_v =0#. This will change with time during its flight by the action of gravitational pull @ #g=10m"/"s^2#

Let after # t# sec from start the particle's velocity velocity makes angle #theta =60^@#with the initial velocity in horizontal direction.
After # t# sec from start its vertical component will be

#V'_v=V_v+txxg=0+10t=10t" "m"/"s#

So #(V'_v)/V_h=tantheta#

#=>(10t)/(20/sqrt3)=tan60^@=sqrt3#

#=>t=2 #sec

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