Question

A projectile is thrown in the vertically upward direction making an angle of 60 with the horizontal direction with a velocity of 150 m/s. the time after which its inclination with the horizontal is 45, is

A)15(√3-1)s B)15(√3+1)s C) 7.5 (√3-1)s D)7.5(√3+1)s

Answer 1

let after time t its inclination with horizontal is 45

at this time Vy /Vx =tan45 or Vy =Vx

Vx remains constant =150cos60 =Vy

now using equation of motion for verticle direction

Vy=Uy-gt..........eq1

Uy=150sin60 ,Uy=150cos60

putting in eq 1,

Vy=150sin60-gt
or, 150cos60=150sin60-gt
or, gt=150sin60-150cos60
or, gt=150(root3/2-1/2)
or, gt=75(root3-1)
or t= (75/10)(root3-1)
=7.5(root3-1)

so answer is option (c)